Question

the scatterplot below shows the association between the amount of time spent studying for a test and the score on the test. a regression line is also shown which models the data.
which statement describes the y - intercept in the context of the situation?
a a student who does not study for the test receives a test score of about 10 points.
b a student receives about 10 points for each additional hour spent studying for the test.
c a student receives about 1 point for every 10 additional hours spent studying for the test.
d a student who studies 10 hours for the test receives a test score of about 0 points

Explanation:

In a regression line equation \(y = mx + b\), the \(y\)-intercept (\(b\)) is the value of \(y\) when \(x = 0\). Here, \(x\) represents time spent studying (in hours) and \(y\) represents test score (in points). When \(x = 0\) (no study time), the \(y\)-value (test score) is approximately \(10\).

• Option A: When \(x = 0\) (no study), \(y\approx10\). This matches the definition of the \(y\)-intercept.
• Option B: This describes the slope (\(m\), rate of change of \(y\) with respect to \(x\)), not the \(y\)-intercept.
• Option C: Incorrectly relates the relationship between \(x\) and \(y\) in a non - \(y\)-intercept context.
• Option D: When \(x = 10\), we are not looking at the \(y\)-intercept (\(x = 0\) for \(y\)-intercept).

Answer:

A. A student who does not study for the test receives a test score of about 10 points.