Question

naomis math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. based on the line of best fit, what quiz score should someone who studied 6 hours expect?

Explanation:

Step1: Find the slope of the line

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Take two points \((0,58)\) and \((2,70)\).
\(m=\frac{70 - 58}{2-0}=\frac{12}{2} = 6\)

Step2: Find the equation of the line

The line is in the form \(y=mx + b\). Since \(b = 58\) (when \(x = 0\)) and \(m = 6\), the equation is \(y=6x+58\).

Step3: Substitute \(x = 6\) into the equation

\(y=6\times6+58\)
\(y = 36+58\)
\(y=94\)

Answer:

\(94\)