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 of best fit

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

Step2: Write the equation of the line

The equation of a line in slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. From the point \((0,58)\), \(b = 58\). So the equation is \(y = 6x+58\)

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

When \(x = 6\), \(y=6\times6 + 58\)
\(y=36+58\)
\(y = 94\)

Answer:

\(94\)