madelyns math teacher plots student grades on their weekly quizzes against the number of hours they say they…
madelyns 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 5 hours expect?
Answer
Explanation:
Step1: Find the slope of the line
The line passes through points $(0,55)$ and $(1,62)$. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 0,y_1=55,x_2 = 1,y_2 = 62$, so $m=\frac{62 - 55}{1-0}=7$.
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 $(0,55)$, the y - intercept $b = 55$. So the equation of the line is $y=7x + 55$.
Step3: Predict the score for 5 hours of study
Substitute $x = 5$ into the equation $y=7x+55$. Then $y=7\times5 + 55=35 + 55=90$.
Answer:
90