Question

carloss 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 89?

Explanation:

Step1: Find the slope of the line

The slope \(m\) formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using points \((0,56)\) and \((4,80)\), we have \(m=\frac{80 - 56}{4-0}=\frac{24}{4} = 6\).

Step2: Find the equation of the line

The slope - intercept form is \(y=mx + b\). Since \(b = 56\) (y - intercept when \(x = 0\)) and \(m = 6\), the equation is \(y=6x+56\).

Step3: Solve for \(x\) when \(y = 89\)

Substitute \(y = 89\) into \(y=6x + 56\). So, \(89=6x+56\). Subtract 56 from both sides: \(89 - 56=6x\), which gives \(33 = 6x\). Then \(x=\frac{33}{6}=5.5\).

Answer:

\(5.5\)