Question

prediction from line of best fit
score: 1/7 penalty: 0.25 off
question
a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what x - value does y = 13?
answer attempt 1 out of 2
x =

Explanation:

Step1: Find the slope of the line

Use two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(4,7)$. Then $m=\frac{7 - 4}{4-0}=\frac{3}{4}$.

Step2: Find the y - intercept

The line passes through $(0,4)$, so the y - intercept $b = 4$.

Step3: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m=\frac{3}{4}$ and $b = 4$, we get $y=\frac{3}{4}x+4$.

Step4: Solve for x when y = 13

Set $y = 13$ in the equation $y=\frac{3}{4}x+4$. Then $13=\frac{3}{4}x+4$. Subtract 4 from both sides: $13 - 4=\frac{3}{4}x$, so $9=\frac{3}{4}x$. Multiply both sides by $\frac{4}{3}$ to solve for x: $x=9\times\frac{4}{3}=12$.

Answer:

$12$