Question

a teacher collected data to see if there was a relationship between how a student performed on a test and how long the student spent studying. a trend line has been drawn for the data. the equation for the line is: y = 0.80x + 59. which best interprets the slope of the linear model?
a a student who studied for 30 minutes is predicted to earn a grade of 80 points.
b a student who did not study for the test is predicted to earn a grade of 59 points.
c each additional minute of study time is associated with an additional 0.8 points on the test.
d each additional 0.80 minutes of study time is associated with an additional point on the test.

Explanation:

Step1: Recall Slope Interpretation

In a linear equation \( y = mx + b \), \( m \) (slope) represents the rate of change of \( y \) with respect to \( x \). Here, \( y \) is test score, \( x \) is study time (minutes), \( m = 0.80 \), \( b = 59 \).

Step2: Analyze Each Option

• Option A: Plug \( x = 30 \) into \( y = 0.80(30)+59 = 24 + 59 = 83

eq 80 \). Eliminate A.

• Option B: When \( x = 0 \) (no study), \( y = 0.80(0)+59 = 59 \). But this is the y - intercept, not slope interpretation. Eliminate B.
• Option C: Slope \( 0.80 \) means for each 1 - minute increase in \( x \) (study time), \( y \) (test score) increases by \( 0.80 \). So each additional minute of study is associated with 0.8 points more. This matches slope interpretation.
• Option D: Slope is change in \( y \) per change in \( x \), not vice - versa. So "each additional 0.80 minutes of study" is incorrect. Eliminate D.

Answer:

C. Each additional minute of study time is associated with an additional 0.8 points on the test.