Question

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?
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Explanation:

Step1: Find the equation of the line of best - fit

Assume the line of best - fit is in the form \(y = mx + b\), where \(y\) is the quiz score, \(x\) is the time spent on homework per week. We can use two points on the line \((x_1,y_1)=(0,58)\) and \((x_2,y_2)=(4,82)\) to find the slope \(m\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

$$m=\frac{82 - 58}{4-0}=\frac{24}{4}=6$$

Since the line passes through \((0,58)\), the \(y\) - intercept \(b = 58\). So the equation of the line is \(y=6x + 58\).

Step2: Predict the quiz score for \(x = 6\)

Substitute \(x = 6\) into the equation \(y=6x + 58\).

$$y=6\times6+58=36 + 58=94$$

Answer:

94