Question

amber created a scatter plot and drew a line of best fit, as shown.
what is the equation of the line of best fit that amber drew?

Explanation:

Step1: Identify two points on the line

We can see that the line passes through (0, 12) (the y - intercept) and another point, say (8, 15) (by looking at the grid, when x = 8, y seems to be 15).

Step2: Calculate the slope (m)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using (0, 12) as $(x_1,y_1)$ and (8, 15) as $(x_2,y_2)$, we have $m=\frac{15 - 12}{8 - 0}=\frac{3}{8}=0.375$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m=\frac{3}{8}$ and $b = 12$ (from the point (0, 12)). So the equation of the line is $y=\frac{3}{8}x + 12$ or $y = 0.375x+12$.

Answer:

$y=\frac{3}{8}x + 12$ (or $y = 0.375x + 12$)