Question

samuels 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 slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,59)$ and $(1,65)$, we have $m=\frac{65 - 59}{1-0}=6$.

Step2: Find the equation of the line

The equation of a line in slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Since the line passes through $(0,59)$, $b = 59$. So the equation of the line is $y=6x + 59$.

Step3: Make a prediction

We want to find the quiz score when $x = 6$. Substitute $x = 6$ into the equation $y=6x+59$. Then $y=6\times6 + 59=36+59 = 95$.

Answer:

95