Question

the equation below represents the trend line of a scatter plot showing the hours spent studying versus science test scores.
y = 6.5x + 42.4

the equation below represents the trend line of a scatter plot showing the hours spent studying versus math test scores.
y = 7.2x + 34.7

if a student does not study for either test, on which test should the student expect the higher score?

○ on the science test because the rate of change is greater
○ on the math test because the rate of change is greater
○ on the science test because the y - intercept is greater
○ on the math test because the y - intercept is greater

Explanation:

Step1: Understand the problem

We need to find which test (science or math) a student who studies 0 hours (x = 0) will score higher on. The equations are in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept (the value of \(y\) when \(x = 0\)).

Step2: Find the y - intercepts

For the science test equation \(y=6.5x + 42.4\), when \(x = 0\) (no studying), \(y=6.5(0)+42.4=42.4\).

For the math test equation \(y = 7.2x+34.7\), when \(x = 0\) (no studying), \(y=7.2(0)+34.7 = 34.7\).

Step3: Compare the y - intercepts

Since \(42.4>34.7\), the y - intercept of the science test trend line is greater. So when \(x = 0\) (no studying), the score on the science test is higher because the y - intercept is greater.

Answer:

on the science test because the y - intercept is greater