carloss math teacher plots student grades on their weekly quizzes against the number of hours they say they…
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, what quiz score should someone who studied 6 hours expect?
Answer
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 $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line of best - fit, say $(0,56)$ and $(1,62)$. Then $m=\frac{62 - 56}{1-0}=6$.
Step2: Find the y - intercept
The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Using the point $(0,56)$ and $m = 6$, when $x = 0$, $y=b$. So $b = 56$. The equation of the line of best - fit is $y=6x + 56$.
Step3: Predict the quiz score for $x = 6$
Substitute $x = 6$ into the equation $y=6x + 56$. Then $y=6\times6+56$. $y = 36+56=92$.
Answer:
92