Question

shane created a scatter - plot and drew a line of best fit, as shown. what is the equation of the line of best fit that shane drew? a. y = 5x + 10 b. y = 5x+11 c. y=\frac{1}{2}x + 10 d. y=\frac{1}{2}x + 11

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Estimate y - intercept

The line of best - fit crosses the y - axis around $y = 10$. So, $b\approx10$.

Step3: Estimate slope

Pick two points on the line, say $(0,10)$ and $(20,20)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{20 - 10}{20-0}=\frac{1}{2}$.

Step4: Write the equation

The equation of the line is $y=\frac{1}{2}x + 10$.

Answer:

C. $y=\frac{1}{2}x + 10$