Question

A coordinate grid shows Number of Classes on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line passes through (0, 10) and a point at (4, 32). The second line passes through (0, 0) and a point at (2, 15). Anna compares Fit Fast and Stepping Up gyms for fitness classes. What is the system of equations representing these costs?

A. ( y = 5.5x ) and ( y = 7.5x + 10 )
B. ( y = 7.5x ) and ( y = 5.5x )
C. ( y = 7.5x ) and ( y = 5.5x + 10 )
D. ( y = 7.5x + 10 ) and ( y = 5.5x + 10 )

Answer 1

The system of equations representing the costs of Fit Fast and Stepping Up gyms is (y = 8x + 10) and (y = 7.5x).

Step-by-step explanation:

The system of equations representing the costs of Fit Fast and Stepping Up gyms can be found by finding the equation of each line.

The first line passes through (0, 10) and (4, 32).

The equation of this line can be found using the formula y = mx + b, where m is the slope and b is the y-intercept.

First, calculate the slope using the formula: m = (y2 - y1) / (x2 - x1) = (32 - 10) / (4 - 0) = 8.

Next, use the slope and one point to find the y-intercept: 10 = 8(0) + b, so b = 10.

Therefore, the equation of the first line is y = 8x + 10.

The second line passes through (0, 0) and (2, 15).

Using the same method, calculate the slope: m = (15 - 0) / (2 - 0) = 7.5.

Then find the y-intercept: 0 = 7.5(0) + b, so b = 0.

Therefore, the equation of the second line is y = 7.5x.

Therefore, the system of equations representing these costs is (y = 8x + 10) and (y = 7.5x).