Question

the scatter plot shows the relationship between the test score, y, out of 100, and the total number of minutes, x, students spend studying for a test. which function best represents the linear model for the data in the scatter plot? options: y = 0.5x + 10, y = 0.5x + 50, y = 2x + 10

Explanation:

Step1: Analyze the trend

The scatter plot shows as \( x \) (minutes) increases, \( y \) (score) increases, so positive slope. Let's check the options: all have positive slopes, so check intercept and slope magnitude.

Step2: Estimate the line

Pick two points. Let's say when \( x = 10 \) (approx), \( y \approx 15 \)? Wait, no, looking at the plot: when \( x = 10 \) (maybe), but better to check the options. Let's take \( x = 0 \), the y-intercept. The line should start around y=10? Wait, the options: \( y = 0.5x + 10 \), \( y = 0.5x + 50 \), \( y = 2x + 10 \). Let's check slope. If \( x \) increases by 20 (from 10 to 30 minutes), \( y \) increases by, say, from 15 to 25? No, wait the plot: when \( x = 10 \) (minutes), \( y \approx 15 \)? Wait, no, the x-axis is minutes (0 - 60), y-axis is score (0 - 80). Let's take two points: suppose at \( x = 10 \), \( y \approx 15 \); at \( x = 50 \), \( y \approx 35 \). Then slope \( m=\frac{35 - 15}{50 - 10}=\frac{20}{40}=0.5 \). Intercept: when \( x = 0 \), \( y \approx 10 \). So the equation is \( y = 0.5x + 10 \).

Answer:

\( y = 0.5x + 10 \) (the first option among the given choices, likely labeled as the option with \( y = 0.5x + 10 \))