#1.) What is the slope between point C and Point D? *Please Show All Work*
#2.) What is the equation of the line (Slope-Intercept Form: y = mx + b) that represents the climb from Point C to Point D? *Please Show All Work*

#3.) What is the domain and range the C to D part of the roller coaster?

Let's see what to do buddy....

_________________________________

1) Go...

We have the following equation for finding the slope of the line by using two points :

[tex]slope = m = \frac{y(b) - y(a)}{x(b) - x(a)} \\ [/tex]

Where a and b are the points which the line through them.

We have points C and D here ,

So :

[tex]slope = m = \frac{y(d) - y(c)}{x(d) - x(c)} \\ [/tex]

D = ( 7 , 12 ) and C = ( 0 , 0 )

Now just need to put the coordinates in the above equation :

[tex]slope = m = \frac{12 - 0}{7 - 0} = \frac{12}{7} \\ [/tex]

_________________________________

2) Go...

We have the following equation to find the point-slope form of the linear functions :

[tex]y - y(o) =(slope) \times ( \: x - x(o) \: ) \\ [/tex]

Where o is one of the given points.

So we must choose one of the points ,

I choose : D = ( 7 , 12 )

Then we have :

[tex]y - 12 = \frac{12}{7}(x - 7) \\ [/tex]

It's point-slope form, so we need to simplifies it to find slope-intercept form.

Look:

[tex]y - 12 = \frac{12}{7}x - 12 \\ [/tex]

Both sides plus 12

[tex]y = \frac{12}{7}x \\ [/tex]

Now we have the slope-intercept form of the CD line.

_________________________________

3) Go...

Domain = [ 0 , 7 ]

Range = [ 0 , 12 ]

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

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