how do you know if the solutions to a quadratic equations are inside, outside, on, inside and on, or outside and on the parabola? with the different equality signs?
Answers
Answer:
Option (1)
Step-by-step explanation:
Given quadratic equation in this question is,
y < -x²+ 4x + 5
Now we will convert this standard quadratic equation into vertex form,
y < -(x² - 4x) + 5
y < -[x² - 2(2)x + 2²] + 5
y < -(x - 2)²+ 5
This equation is in the form of y < a(x - h)² + k
where (h, k) is the vertex of the parabola.
Therefore, y < -(x - 2)²+ 5 will show the parabola with properties as,
1). Parabola having vertex at (2, 5).
2). Coefficient 'a' is negative, so parabola will open downwards.
3). In the inequality notation of less than, (sign < ) will show the solution area inside the parabola.
[If an inequality has a sign of greater than, solution area will be outside the parabola.]
Therefore, Option (1) will be the answer.
Related Questions
the population of a village is 15000.among them 9000 read kantipur,75000 read gorkhapatra and 40%read both the magazines.find the percent of people who dont read both the magazines.
Answers
Answer:
30%
Step-by-step explanation:
Total population=15,000
kantipur=9000
gorkhapatra= 7500
Both magazine=40%
n(k intersection g)=40% of 15,000
=0.4*15,000
=6,000
n(k) =9000
n(g)=7500
n(A union B)= n(k) + n(g) -n(k intersection g)
=9000+7500-6000
=10,500
Population who do no read= Total population - n(A union B)
=15000-10500
=4500
Percentage population who do not read both magazine
=4,500/15,000 * 100
=0.3 * 100
=30%
Find the values for which the statement is true and mark them on the number line: |x|=x
Answers
Answer:
The function f(x) = IxI works as follows:
if x ≤ 0, then IxI = -x
if x ≥ 0, then IxI = x
notice that if x = 0, then I0I = 0 = -0
Now, we want that:
IxI = x
Then we have that x must be greater or equal than zero:
x ≥ 0.
To represent it in the number line, you should use a black dot in the zero an shade all the right region:
__-2__-1__0__1__2__3__4__5__6__....
If you get a penny a day from your uncle and each day he doubles the amount he gave you on the previous day how much would he give you on the twentieth day
Answers
Answer: On the 20th day, he will give $5242.88
Step-by-step explanation: This is a geometric series with elements:
initial value ([tex]a_{0}[/tex]) = 0.01
ratio = 2
At the twentieth day means the 20th term, i.e. n = 20.
To determine that term, use the formula: [tex]a_{n} = a_{0}.r^{n-1}[/tex]
Substituing terms:
[tex]a_{20} = 0.01.2^{20-1}[/tex]
[tex]a_{20} = 0.01.2^{19}[/tex]
[tex]a_{20} = 0.01.524288[/tex]
[tex]a_{20} = 5242.88[/tex]
Then, on the 20th day, your uncle gave to you $5242.88
What the answer to the question
Answers
Answer:
6.1
Step-by-step explanation:
use law of cosines
d² = e² + f² - 2ef cos D
d² = 9² + 10² - 2(9)(10) cos 37
d² = 81 + 100 - 143.75
d² = 37.25
d = 6.1
Find the value of y.
A.
[tex] \sqrt{55} [/tex]
B. 6
C.
[tex]8 \sqrt{3} [/tex]
D.16
Answers
Answer:
[tex]y=\sqrt{55}[/tex]
which agrees with answer A
Step-by-step explanation:
Notice there are three right angle triangles for which we can apply the Pythagorean theorem:
In the small triangle at the bottom we have the Pythagorean theorem rendering:
(a)
[tex]5^2+y^2=x^2\\x^2=25+y^2[/tex]
in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:
(b)
[tex]11^2+y^2=z^2\\z^2=121+y^2[/tex]
and finally in the large right angle triangle:
(c)
[tex]z^2+x^2=16^2\\z^2=256-x^2[/tex]
We can combine equations b and c to obtain:
[tex]121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2[/tex]
and then combine this and (a) to get:
[tex]25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=\sqrt{55}[/tex]
Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below. (1 – 3x) = 4(– + 2) 4 lines of math. The first line is, StartFraction 5 Over 6 EndFraction left-parenthesis 1 minus 3 x right-parenthesis equals 4 left-parenthesis negative StartFraction 5 x Over EndFraction plus 2 right-parenthesis. The second line is, StartFraction 5 Over 6 EndFraction minus StartFraction 5x Over 2 EndFraction equals StartFraction 5x Over 2 EndFraction plus 8. The third line in plus StartFraction 5x Over 2 EndFraction and StartFraction 5x Over 2 EndFraction on both sides of the equal sign. The fourth line is 0 equals x. 0 = x
Answers
Answer:
Micah's solution is wrong
Step-by-step explanation:
Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below.
(1 – 3x) = 4(– + 2)
0 = x
Which statement is true about Micah’s solution?
Micah’s solution is wrong.
There are no values of x that make the statement true.
Micah’s solution is correct, and the value of x that makes the statement true is 0.
Micah should have divided by .
Micah should have subtracted
Solution
First solve for the value of x
Given
(1 – 3x) = 4(– + 2)
It could mean; (1 – 3x) = 4(+ 2)
or
(1 – 3x) = 4(-2)
In the first option (1 – 3x) = 4(+ 2)
1 – 3x = 4(+ 2)
1-3x= 8
-3x=8-1
-3x=7
x= -7/3
In the second option
(1 – 3x) = 4(-2)
1-3x= -8
-3x= -8-1
-3x = -9
x= 3
x= 3 0r -7/3
The values of x that make the statement true are 3 and -7/3
Micah's solution of x=0 is wrong
Answer:
A. Micah’s solution is wrong. There are no values of x that make the statement true.
Step-by-step explanation:
T models the temperature (in degrees Celsius) in New York City when it's t hours after midnight on a given day. Match each statement with the feature of the graph that most closely corresponds to it.
Answers
Answer:
Please check explanation
Step-by-step explanation:
Here, we want to do a matching.
We shall be matching the given statements with the features we have on the graph
Hence we shall be looking closely at the graph to answer the questions.
The y-intercept is the point at which the graph touches the y-axis
And it was at -3 degrees celsius at the beginning of the day.
The temperature was above zero between 8am and 8pm. The matching statement is that it is increasing or decreasing interval
We can see that the graph rose from 8am before it finally comes to zero at 8pm
Positive or negative interval matches with it was getting warmer between 2am and 2pm.
While temperature was lowest at 2am, we can see a peak at 2pm.
An education researcher claims that 58% of college students work year-round. In a random sample of 400 college students, 232 say they work year-round. At alphaequals0.01, is there enough evidence to reject the researcher's claim? Complete parts (a) through (e) below.
Answers
Answer:
The proportion of college students who work year-round is 58%.
Step-by-step explanation:
The claim made by the education researcher is that 58% of college students work year-round.
A random sample of 400 college students, 232 say they work year-round.
To test the researcher's claim use a one-proportion z-test.
The hypothesis can be defined as follows:
H₀: The proportion of college students who work year-round is 58%, i.e. p = 0.58.
Hₐ: The proportion of college students who work year-round is 58%, i.e. p ≠ 0.58. C
Compute the sample proportion as follows:
[tex]\hat p=\frac{232}{400}=0.58[/tex]
Compute the test statistic value as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0[/tex]
The test statistic value is 0.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
Compute the p-value for the two-tailed test as follows:
[tex]p-value=2\times P(z<0)=2\times 0.5=1[/tex]
*Use a z-table for the probability.
The p-value of the test is 1.
The p-value of the test is very large when compared to the significance level.
The null hypothesis will not be rejected.
Thus, it can be concluded that the proportion of college students who work year-round is 58%.
please Evaluate ( 8/3) to the 2 power A). 8/9 B). 64/9 C). 64/3 D). 55
Answers
Answer:
64/9
Step-by-step explanation:
(8/3) ^2
( 8/3) * (8/3)
64/9
64/9 is the answer <3<3 Hope this helps
1. A test-tube has a diameter of 3cm. How many turns would a piece of thread of length
90.42cm make round the test tube. (Taken= =).
(3marks)
Answers
So if we think of a test tube, it looks sort of like a cylinder. This means that its cross-section would be a circle. To find out how many turns a piece of thread would make around the test tube, we need to find the circumference of the test tube, then divide the length of the string by the circumference.
Step 1) Find the circumference
C = pi x diameter
C = 3.14 x 3
C = 9.42
Step 2) Divide the length of the string by the circumference
90.42 / 9.42 = 9.5987
The string would make approximately 9.60 turns around the test tube.
Hope this helps!! :)
Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and
16 minutes to lay down 44 cubic yards of mulch.
Plot five data points and the line that represent this direct variation relationship.
Answers
Answer with explanation:
Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and 16 minutes to lay down 44 cubic yards of mulch.
Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.
Let k be the constant of proportionality, such that
[tex]k=\dfrac{y}{x}[/tex]
For x= 4 and k= 11, [tex]k=\dfrac{11}{4}[/tex]
Required equation: [tex]y=\dfrac{11}{4}x[/tex]
Two points are given in question: (4,11) , (16,44).
Take x= 8 , [tex]y=\dfrac{11}{4}(8)=22[/tex]i.e. point (8,22)
Similarly, for x= 12, y=33 i.e. point (12, 33)
For x= 20 , y= 55 i.e. point (20,55)
Five data points: (4,11) , (16,44), (8,22), (12, 33), (20,55).
Now, we plot these points on graph and join them
Answer:
Here
Step-by-step explanation:
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
Answers
Answer:
y=x+2
Step-by-step explanation:
I have included a graph with the equation and both points on it (click/tap on it to see the full picture.)
Answer: y= x+2
Step-by-step explanation:
Calculate the shaded region
Answers
｡☆✼★ ━━━━━━━━━━━━━━ ☾
First find the area of the sector.
For that, use this equation:
area = [tex]\frac{x }{360} * \pi r^{2}[/tex]
where 'x' is the angle and 'r' is the radius
Sub the values in
area = [tex]\frac{56}{360} * \pi15^2[/tex]
Solve:
area = [tex]35\pi[/tex]
It is easier to keep it in terms of pi until the end
Now, calculate the area of the triangle within the sector
area = 1/2 ab x sinC
where 'a' and 'b' are the radius (side lengths) and C is the angle
thus,
area = 1/2(15 x 15) x sin(56)
area = 93.27 (to 2 d.p)
Now subtract the area of the triangle from the area of the sector
[tex]35\pi[/tex] - 93.27 = 16.6857
This would give you a final answer of 16.69 units^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
30 POINTS!!!
Suppose f(x) = x2 and
g(x) = (1/3)^2. Which statement best compares the graph of g(x) with the graph of f(x)?
Image attached
Please help!!!
Answers
Answer:
A. The graph of g(x) is vertically compressed by a factor of 3.
Step-by-step explanation:
When there is a fraction, that means that there is a veritcal dilation.
Hope this helps! Good luck!
A life insurance company sells a $100,000 one year term life insurance policy to a 30-year old male for $475. The probability that the male survives the year is .999172. Find the expected value for the insurance company.
Answers
Answer:
The expected value for the insurance company is $392.20.
Step-by-step explanation:
The expected value of a random variable, X is:
[tex]E(X)=x\cdot P(X)[/tex]
It is provided that a life insurance company sells a $100,000 one year term life insurance policy to a 30-year old male for $475.
The probability that the male survives the year is, P(S) = 0.999172.
Then the probability that the male does not survives the year is:
P (S') = 1 - P (S)
= 1 - 0.999172
P (S') = 0.000828
The amount the company owes the male if he survives is, S = $475.
The amount the company owes the male if he does not survives is,
S' = $475 - $100,000 = -$99525.
Compute the expected value for the insurance company as follows:
[tex]E(\text{Insurance Company})=S\cdot P(S)+S'\cdot P(S')[/tex]
[tex]=(475\times 0.999172)+(-99525\times 0.000828)\\=474.6067-82.4067\\=392.20[/tex]
Thus, the expected value for the insurance company is $392.20.
15. To save for retirement, Karla Harby put $625 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $156 comma 700. What annual interest rate did she receive? The interest rate she received was approximately _______%. (Round to two decimal places as needed.)
Answers
Answer:
40.08%
Step-by-step explanation:
From the given information;
the annual interest rate can be determined using the formula:
[tex]A =P \times( 1+ \dfrac{r}{n})^{nt}[/tex]
where;
A = amount
P is the installment per period = $625
r = interest rate
nt = number of installments= 14×(12) =168
i = rate of interest per year
[tex]156700 = 625 \times( 1+ \dfrac{r}{12})^{168}[/tex]
[tex]\dfrac{156700}{625} = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]250.72 = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]\sqrt[168]{250.72} = {(1+ \dfrac{r}{12})[/tex]
1.0334 = [tex]{(1+ \dfrac{r}{12})[/tex]
1.0334 -1 = r/12
0.0334 = r/12
r = 0.0334 × 12
r = 0.4008
r = 40.08%
Thus; Karla Harby received an interest rate of 40.08%
Select the correct answer.
Which relation is a function?
Answers
a function will not have any repeating x values...they all have to be different...they can have repeating y values, just not repeating x values.
so ur answer is : { (-1,5), (-2,6), (-3,7) }...u see how there is no repeating x values....this is a function....the other 3 are not.
a sector with a radius of 12cm has an area of 60pi cm what is the central angle in radians
Answers
Answer:
5/6π.
Step-by-step explanation:
The following data were obtained from the question:
Radius (r) = 12 cm
Area (A) = 60π cm²
Centre angle in radian (∅) =...?
Since we are to look for the centre angle in radian, the area of the sector will be given by:
A = ½r²∅
Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:
A = ½r²∅
60π = ½ × 12² × ∅
60π = ½ × 144 × ∅
60π = 72 × ∅
Divide both side by 72
∅ = 60π/72
∅ = 5/6π
Therefore, the centre angle measured in radian is 5/6π.
Find the measure of d.
Answers
Answer:
[tex] d = 123 [/tex]
Step-by-step explanation:
The given figure above is an inscribed quadrilateral with all four vertices lying on the given circle, thereby forming chords each.
Therefore, the opposite angles of the above quadrilateral are supplementary.
This means:
[tex] c + 31 = 180 [/tex] , and
[tex] d + 57 = 180 [/tex]
Find the measure of d:
[tex] d + 57 = 180 [/tex]
Subtract 57 from both sides.
[tex] d + 57 - 57 = 180 - 57 [/tex]
[tex] d = 123 [/tex]
Can someone help me with this one too
Answers
Answer:
A. [tex] 3 {}^{9} [/tex]
Step-by-step explanation:
[tex]3 {}^{4} \times {3}^{5} = {3}^{4 + 5} = 3 {}^{9} [/tex]
Hope this helps ;) ❤❤❤
Answer:
[tex]\boxed{3^9}[/tex]
Step-by-step explanation:
[tex]3^5 \times 3^4[/tex]
Apply the law of exponents : [tex]a^b \times a^c = a^{b+c}[/tex]
The exponent product rule states that, when multiplying two exponents that have the same base, you can add the exponents.
[tex]3^{5+4}[/tex]
[tex]3^9[/tex]
Find the length of BC round answer to the nearest hundredth
Answers
Step-by-step explanation:
Use law of sines.
16 / sin 39° = BC / sin 120°
BC ≈ 22.02
Greetings from Brasil...
Here we cant use calculator..... It seems that in the USA the use of a scientific calculator is allowed
Let's use Senos Law in Any Triangle
(AC/SEN B) = (BC/SEN A)
16/SEN 39 = BC/SEN 120 sen 120 = sen 60 = √3/2
16/0,63 = BC/(√3/2)
0,63BC = 16√3/2
BC = 8√3/0,63
BC ≈ 22Check
Which expressions are a sum or difference of cubes? Sort each expression into the correct category.
64x3 - 216
Sum or Difference of Cubes
Not a Sum or Difference of Cubes
8x9 +27
x3 + 125
36x3 - 121
x6 - 16
Answers
Answer:
The answer to your question is given below.
Step-by-step explanation:
To which of the above expression is a sum or difference of cube, or not a sum or difference of cube, we shall do the following simplification:
Note: The Cube root of a particular number is simply a multiplication of an identical number in three places.
64x³ – 216
64 has a cube root of 4 and 216 has a cube root of 6. Therefore, the above expression can be written as:
4³x³ – 6³
(4x)³ – 6³
64x³ – 216 = (4x)³ – 6³
Therefore, 64x³ – 216 can be expressed as a difference of cube.
8x^9 + 27
8 has a cube root of 2, x^9 has a cube root of x³ and 27 has a
cube root of 3. Therefore, the above expression can be written as:
2³(x³)³ + 3³
(2x³)³ + 3³
8x^9 + 27 = (2x³)³ + 3³
8x^9 + 27 can be expreessed as a sum of cube
x³ + 125
125 has a cube root of 5. Therefore, the above expression can be written as:
x³ + 5³
x³ + 125 = x³ + 5³
x³ + 125 can be expressed as a sum of cube
36x³ + 121
36 and 121 has no cube root. Therefore, the above expression is not a sum or difference of cube.
x^6 – 16
x^6 has a cube root of x² and 16 has no cube root. Therefore, the above expression is not a sum or difference of cube.
Summary:
Sum or Difference of cubes
64x³ – 216
8x^9 + 27
x³ + 125
Not a Sum or Difference of cubes
36x³ + 121
x^6 – 16
Answer:
look at attached picture
The radius of the base of the cone is an 5cm
and slant height is 9cm
Find out its total
surface area
area.
Answers
Answer:
The total surface area of cone is 70π cm² or 219.9 cm².
Step-by-step explanation:
Given that the formula of total surface area of cone is T.S.A = πr² + πrl where r represents radius and l is slant height. So you have to substitute the values :
[tex]t.s.a = \pi {r}^{2} + \pi{r}l[/tex]
[tex]let \: r = 5 \: , \: l = 9[/tex]
[tex]t.s.a = \pi {(5)}^{2} + \pi(5)(9)[/tex]
[tex]t.s.a = 25\pi + 45\pi[/tex]
[tex]t.s. a = 70\pi \: or \: 219.9 \: [/tex]
Plz help mw 8 am so dumb lol
Answers
Answer:
1,1,3,1,1
Step-by-step explanation:
Answer:
0 1
1 1
2 3
3 1
4 1
Step-by-step explanation:
You would just count how many 0 there are in the set and there are 1 and you would put in by 0. For 1 there are 1, for 2 there are 3, for 3 there are 1, and for 4 there are 1.
Please Help asap!!! Please give explanation
Answers
Answer:
The answer is B CPCT
Step-by-step explanation:
In an isosceles triangle ΔHKJ with
Construct KM, a bisector of the base HJ.
to prove:
in ΔKHM and ΔKJM
bisects [Given]
Segment bisectors states that a line or segment which cuts another line segment into two equal parts.
then, by definition of Segment bisector :
[Given]
Reflexive property of congruence that any geometric figure is congruent to itself.
[by definition of Reflexive property of congruence]
SSS(Side-Side-Side) Postulates states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
therefore, by SSS postulates
ΔKHM ΔKJM
By CPCT [Corresponding Part of congruent Triangle]
proved!
hope i helped
-lvr
What is the maximum value of the function
Answers
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]f(x)=-x^2+6x+1[/tex]
x coordinate:
[tex]\frac{-b}{2a}[/tex]
[tex]a=-1\\b=6[/tex]
[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]
y-coordinate:
[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]
Answer:
10
Step-by-step explanation:
Find the common ratio of the geometric sequence: 2/3,−2,6,…
Answers
Answer:
-3
Step-by-step explanation:
Well to find the common ratio we need to figure out,
what * 2/3 = -2.
To find that we do -2 ÷ 2/3
= -3
To check -2 * -3 should be 6 which it is.
Thus,
the common ratio is -3.
Hope this helps :)
Answer:
-3
Step-by-step explanation:
Common ratio = 2nd term ÷ 1 st term
= -2 ÷ 2/3
= [tex]-2 * \frac{3}{2}\\\\[/tex]
= -3
YoIn a sale, the normal price of a book is reduced by 30%. The sale price of the book is £2.80 Work out the normal price of the book.
Answers
Answer: £4
Step-by-step explanation:
From the question, we are informed that when the normal price of a book is reduced by 30%, then the sale price of the book is £2.80.
Since the normal price of a book is reduced by 30%, that means the book is sold at (100% - 30%) = 70% of its normal price.
Let the normal price of the book be y.
70% of y = £2.80
70/100 × y = £2.80
0.7 × y = £2.80
0.7y = £2.80
y = £2.80/0.7
y = £4
The normal price of the book is £4.
PLEASE HELP! Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes will affect the volume of the following shapes: prisms, cylinders, cones and spheres.
Answers
Answer:
An example of a prism could be a an amazon box to represent a rectangular prism. As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.
An example of a cone would be an ice cream cone. As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.
An example of a cylinder could be a cup. As the height or the radius of the cup increases, the larger the volume. More drink for you.
An example of a sphere would be a soccer ball. As the radius increases, the volume of the ball increases. Hence, larger soccer balls have a bigger radius than smaller soccer balls. This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).
Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.
Step-by-step explanation:
Let's simply look at the equations of each shape.
Volume of a prism = base * height
Volume of a cone = Pi * r^2 * (height/3)
Volume of a cylinder = Pi * r^2 * height
Volume of a sphere = (4/3) Pi r^3
Notice that the volumes of prisms, cones, and cylinders directly correlate to height. As height increases, the volume increases. The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius. Consider if you expanded the radius of the sphere, the volume will increase.
Answer:
Increase or decrease the dimensions of objects. See below for an explanation!
Step-by-step explanation:
An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.
A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.
An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.
A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.
You may also shrink the dimensions for each of these objects to make them smaller.
Hope this helps!
What is x - 3y = -9 in function form??? Help!
Answers
This is basically in the form y = mx+b with m = 1/3 as the slope and b = 3 as the y intercept. I'm using f(x) in place of y to indicate function notation.
==========================================
Work Shown:
The goal is to solve for y.
x - 3y = -9
-3y = -9-x ... subtracting x from both sides
-3y = -x-9
y = (-x-9)/(-3) .... dividing both sides by -3
y = -x/(-3) - 9/(-3) ... break up the fraction
y = (1/3)x + 3 .... simplify
f(x) = (1/3)x + 3 .... replace y with f(x)