Question

williams 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, how much time should someone study to expect a quiz score of 94? (chart: y-axis is quiz score, x-axis is time spent on homework per week (hours). points on line: (0,58), (2,70), (4,82))

Explanation:

Step1: Find the slope of the line

The line passes through \((0, 58)\) and \((2, 70)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{70 - 58}{2 - 0}=\frac{12}{2} = 6\).

Step2: Determine the equation of the line

Using the slope - intercept form \(y=mx + b\), where \(b = 58\) (from the point \((0,58)\)) and \(m = 6\), the equation is \(y=6x + 58\).

Step3: Solve for \(x\) when \(y = 94\)

Substitute \(y = 94\) into the equation \(94=6x + 58\).
Subtract 58 from both sides: \(94-58=6x\), so \(36 = 6x\).
Divide both sides by 6: \(x=\frac{36}{6}=6\).

Answer:

6 hours