The Palm Beach High Swimming Team is holding a car wash to raise money
for the team's banquet. All of the supplies for the car wash were donated by
parents of the team members. The graph below represents the situation.
SWIM TEAM CAR WASH
How much did the swim team charge for each car that it washed?
How much money did the swim team have in its account before the car wash?
If the team wants to earn $300, how many cars do they need to wash?

Answer:

Step-by-step explanation:

From the graph attached,

Relation between the amount of money raised and number of car washed is represented by a straight line.

Let the equation of the line is,

y = mx + b

where m = slope of the line = charges for each car wash

b = y-intercept = Initial amount the team have before the car wash.

Slope of the line will define the charges of car wash for each car.

Since, slope of the line passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (0, 100) and (10, 150) will be,

m = [tex]\frac{150-100}{10-0}[/tex]

m = 5

Therefore, charges of each car wash will be = $5

y-intercept of the line 'b' = 100

Equation of the line will be,

y = 5x + 100

If team wants to earn $300,

300 = 5x + 100

5x = 200

x = 40

Therefore, 40 cars will be needed to wash by the swim team to earn $300.

1) The amount of money the swim team charged for each car that it washed is; $5 per car

2) The amount of money that the swim team had in its account before the car wash is; $100

3) If the team wants to earn $300, then number of cars they need to wash is; 40 cars

We know that formula for slope between two points is;

m = (y₂ - y₁)/(x₂ - x₁)

Let us take 2 coordinates from the given graph which are;

(10, 150) and (30, 250)

Thus;

m = (250 - 150)/(30 - 10)

m = 100/20

m = 5

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

From our graph, the y-intercept is 100. Thus, equation of the line of the graph is;

y = 5x + 100

A) From our equation y = 5x + 100, we can say that number of cars are x and as such amount charged per car is $5 per car.

B) The amount of money the swim team had before washing cars is when the value of x is 0. Thus;

y = 5(0) + 100

y = $100

C) The team wants to earn $300 and so we will plug 300 for y into y = 5x + 100 to get;

300 = 5x + 100

5x = 300 - 100

5x = 200

x = 200/5

x = 40 cars.

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