Question

1. jesse collects data on his math scores on the last 12 tests and the number of hours he spent completing his math homework assignments and studying in the week before every test. he creates a scatter plot to show the data. the line shown on the graph best models the data on the scatter plot. based on the given model, how many hours in the week before the test does jesse need to study to get a score of 80 on the test? round your answer to the nearest hour. hours

Explanation:

Step1: Find the slope of the line

We can see two points on the line: when \( x = 0 \) (time studying = 0 hours), \( y = 30 \) (score = 30), and when \( x = 4 \) (assuming the first non - zero x - value with a clear point), \( y = 40 \). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{40 - 30}{4 - 0}=\frac{10}{4}=2.5 \). The equation of the line in slope - intercept form \( y=mx + b \), where \( b = 30 \) (y - intercept), so the equation is \( y = 2.5x+30 \).

Step2: Solve for x when y = 80

We set \( y = 80 \) in the equation \( 80=2.5x + 30 \).
Subtract 30 from both sides: \( 80 - 30=2.5x \), so \( 50 = 2.5x \).
Then divide both sides by 2.5: \( x=\frac{50}{2.5}=20 \).

Answer:

20