Question

select the correct equation. 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 sign

The line of best - fit in the scatter - plot has a negative slope. For a linear equation $y = mx + b$, when $m\lt0$, the line slopes downwards from left to right. Among the given equations, $y=-x + 2$ and $y=-\frac{5}{7}x+2$ have negative slopes, while $y = x + 2$ has a positive slope and $y=\frac{5}{7}x+2$ has a positive slope.

Step2: Estimate slope magnitude

The line of best - fit in the scatter - plot seems to have a slope close to $- 1$. The slope of $y=-x + 2$ is $m=-1$ and the slope of $y =-\frac{5}{7}x+2$ is $m =-\frac{5}{7}\approx - 0.71$. The line in the scatter - plot appears to have a steeper slope (closer to $-1$) compared to a slope of $-\frac{5}{7}$.

Answer:

$y=-x + 2$