Question

Which equation is modeled by the graph? Using the equation, about how many more cars are in the deck at 9:00 a.m. than at 8:30 a.m.?

A) y = 3x + 50; 90 cars
B) y = 4x + 50; 75 cars
C) y = x + 50; 100 cars
D) y = 3x - 50; 120 cars

Answer 1

y = 3x + 50

Explanation:

Substitute the y-intercept (0, 50) and an estimated point (40, 170) into the slope formula and simplify.

m =

y2 - y1

x2 - x1

m =

170 - 50

40 - 0

m = 3

Substitute slope and y-intercept into slope- intercept form.

y = mx + b

y = 3x + 50

The slope represents the change in the number of cars in the parking garage per minute, which is 3.

To find the number of cars in the parking garage at 8:30 a.m., substitute 30 into the equation for x (number of minutes after 8:00 a.m.) and simplify:

y = 30(3) + 50 = 140

To find the number of cars in the parking garage at 9:00 a.m., substitute 60 into the equation for x (number of minutes after 8:00 a.m.) and simplify:

y = 60(3) + 50 = 230

Find the difference: 230 - 140 = 90 cars

Answer 2

The correct answer is Choice A.

You can see from the graph that the y-intercept is 50 because it cross on the left at 50.

To find the slope, we can use the following two points (0, 50) and (20, 110). This will give a slope of 3.

Put the 50 and 3 together and you will have the equation:
y = 3x + 50