Question

samanthas 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 line passes through points $(0, 57)$ and $(4.5, 87)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{87 - 57}{4.5-0}=\frac{30}{4.5}=\frac{20}{3}$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the point $(0,57)$, $b = 57$.

Step3: Write the equation of the line

The equation of a line is $y=mx + b$. Substituting $m=\frac{20}{3}$ and $b = 57$, we get $y=\frac{20}{3}x+57$.

Step4: Predict the score for 6 hours

Substitute $x = 6$ into the equation $y=\frac{20}{3}\times6+57$. First, $\frac{20}{3}\times6 = 40$. Then $y=40 + 57=97$.

Answer:

97