Question

Renee is comparing catering costs for her wedding. Which system of equations correctly represents the graph below?

Options:
A. y = 10x + 800, y = 15x + 400
B. y = 10x + 400, y = 15x + 800
C. y = -10x + 800, y = -15x + 400
D. y = 1/2x + 800, y = 3/4x + 400

Answer 1

The correct system of equations that represents the given graph is Option A: y = 10x + 800, y = 15x + 400. The first equation has a slope of 10 and a y-intercept of 800, while the second equation has a slope of 15 and a y-intercept of 400.

Step-by-step explanation:

The correct system of equations that represents the given graph is Option A: y = 10x + 800, y = 15x + 400.

To determine the correct system of equations, we need to analyze the slope-intercept form, y = mx + b. In the graph, we can see that the slope of the line is steeper for the catering cost of $15 per person, and less steep for the catering cost of $10 per person. So, the first equation should have a slope of 10, and the second equation should have a slope of 15.

Moreover, the y-intercepts of the lines indicate the additional costs for the wedding. In the graph, the y-intercepts are 800 for the first line and 400 for the second line. Therefore, the correct system of equations is y = 10x + 800, y = 15x + 400.