Question

identify the equation that represents the line of best fit on this scatter plot.
$y=-x + 2$
$y=x + 2$
$y=\frac{5}{7}x + 2$
$y=-\frac{5}{7}x + 2$

Explanation:

Step1: Determine slope

The line has a positive slope as it rises from left - to - right. For a line $y = mx + b$, $m$ is the slope. The slope of $y=-x + 2$ is $m=-1$ and of $y =-\frac{5}{7}x+2$ is $m =-\frac{5}{7}$, which are negative, so we can eliminate them.

Step2: Estimate slope value

We can use two points on the line (e.g., $(0,2)$ and $(7,7)$). The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{7 - 2}{7-0}=\frac{5}{7}$.

Step3: Determine y - intercept

The line intersects the y - axis at $y = 2$, so the y - intercept $b = 2$. The equation of the line is $y=\frac{5}{7}x+2$.

Answer:

$y=\frac{5}{7}x + 2$