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 85?

Explanation:

Step1: Find the slope of the line

Use the two - point formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,54)\) (the \(y\) - intercept) and \((x_2,y_2)=(3.4,79)\).

$$m=\frac{79 - 54}{3.4-0}=\frac{25}{3.4}\approx7.35$$

The equation of the line in slope - intercept form is \(y = mx + b\), where \(b = 54\). So \(y=7.35x + 54\)

Step2: Solve for \(x\) when \(y = 89\)

Substitute \(y = 89\) into the equation \(89=7.35x + 54\)

$$7.35x=89 - 54$$

$$7.35x=35$$

$$x=\frac{35}{7.35}\approx4.76$$

Answer:

A person should study approximately \(4.8\) hours.