Question

williams 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, how much time should someone study to expect a quiz score of 94?

Explanation:

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

Assume the line of best - fit has the form $y = mx + b$, where $y$ is the quiz score, $x$ is the time spent on homework per week, $m$ is the slope and $b$ is the y - intercept. We can use two points on the line, say $(0,58)$ and $(4,82)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{82 - 58}{4-0}=\frac{24}{4}=6$. Using the point - slope form with the point $(0,58)$ (where $x_1 = 0,y_1 = 58$), the equation of the line is $y=6x + 58$.

Step2: Find the value of $x$ for a quiz score of 94

Set $y = 94$ in the equation $y=6x + 58$. Then $94=6x + 58$.
Subtract 58 from both sides: $94−58=6x$, so $36 = 6x$.
Divide both sides by 6: $x=\frac{36}{6}=6$.

Answer:

6