Question

After 4 hours, a car wash fundraiser had raised $180. After 6 hours, the students had raised $280. Assuming a linear function, write an equation in the form y=mx+b that shows the profit earned washing cars for x hours.

Answer 1

Explanation:

(1) Formally....

The two data points are (4,180) and (6,280).

The slope is (y2-y1)/(x2-x1) = (280-180)/(6-4) = 100/2 = 50; so the equation is y = 50x+b.

Use either data point (I chose the first) to determine the value of b:

180+=+50%284%29%2Bb

180+=+200%2Bb

b+=+-20

The equation is y = 50x-20.

Informally....

(You should understand that the algebraic solution is just a formalization of common sense.)

The additional 2 hours brought in an additional $100; the rate is $50 per hour.

After 4 hours, the actual dollar amount was $180. $50 per hour for 4 hours would be $200; so the dollar amount is $20 less than $50 per hour.

$20 less than $50 per hour in algebraic notation is

50x-20

Answer 2

First we need to find the slope of the linear function. To do so, we can use the following equation:

m = (y1 - y2) / (x1 - x2)

where (x1, y1) and (x2, y2) are the two points.

In this case, time in hours is along the x-axis, and money in dollars is along the y-axis.

The two points are (4 hours, $180) and (6 hours, $280). Now plug the values into the slope equation:

m = (180 - 280) / (4 - 6) = (-100)/(-2) = 100/2 = 50.

Now plug one of the points and the slope into the equation for point-slope form:

y - y1 = m (x - x1)

y - 180 = 50(x - 4)

Solve for y to get the equation in slope intercept form:

y - 180 = 50x - 200


ANSWER:


y = 50x - 20