select the correct equation. identify the equation that represents the line of best fit on this scatter…

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

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

Answer

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:

$y=-x + 2$