Question

josephs 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

The line of best fit passes through the points \((0, 57)\), \((2, 69)\), and \((4, 81)\). We can use two points, say \((0, 57)\) and \((2, 69)\), to find the slope \(m\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 0\), \(y_1 = 57\), \(x_2 = 2\), \(y_2 = 69\) into the formula:
\(m=\frac{69 - 57}{2 - 0}=\frac{12}{2}=6\)

Step2: Determine the equation of the line

The line has a y - intercept \(b = 57\) (since it passes through \((0, 57)\)) and a slope \(m = 6\). The equation of a line in slope - intercept form is \(y=mx + b\). So the equation of the line of best fit is \(y = 6x+57\).

Step3: Find the quiz score for \(x = 6\) hours of study

Substitute \(x = 6\) into the equation \(y = 6x + 57\):
\(y=6\times6 + 57\)
\(y = 36+57\)
\(y=93\)

Answer:

93