Question

The equations y = -2.5x + 15 and 25x + 10y = 150 represent Hanna’s music festival situation. Is it easier to find the x-intercept of the graph of the equations using slope-intercept or standard form?

A. Slope-intercept form is easier.
B. Standard form is easier.
C. Both forms are equally easy.
D. It depends on the specific situation.

Answer 1

To find the x-intercept, the slope-intercept form is easier to use than the standard form. It involves setting y to zero and solving directly for x, which is more straightforward than rearranging the standard form equation.

Step-by-step explanation:

A student has asked whether it's easier to find the x-intercept of the graph of the equations using slope-intercept form or standard form. The slope-intercept form is given by y = -2.5x + 15, and the standard form is 25x + 10y = 150. In slope-intercept form, finding the x-intercept is straightforward because you can set y to zero and solve for x. The x-intercept will be when y=0, thus x = 15/(-2.5) = -6. In contrast, with the standard form, one would need to rearrange the equation to solve for y first (10y = -25x + 150) and then set y to zero to solve for x, which is a bit more work.

Given this, the more convenient form for finding the x-intercept is the slope-intercept form, as it requires less manipulation. Therefore, the answer to the student's question is A. Slope-intercept form is easier.