xcopyv4n

2023-03-07

How to find an equation of the line containing the given pair of points(-7, -4) and ( -2, -6)?

Nhluvukoj6m

First, we need to determine the slope of the line running through the two points. The slope can be found by using the formula: $m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$
Where $m$ is the slope and (${x}_{1},{y}_{1}$) and (${x}_{2},{y}_{2}$) are the two points on the line.
The result of substituting the values from the problem's points is:
$m=\frac{-6--4}{-2--7}=\frac{-6+4}{-2+7}=\frac{-2}{5}=-\frac{2}{5}$
We can now use the point-slope formula to write and equation for the line. The point-slope formula states: $\left(y-{y}_{1}\right)=m\left(x-{x}_{1}\right)$
Where $m$ is the slope and $\left(\begin{array}{cc}{x}_{1}& {y}_{1}\end{array}\right)$ is a point the line passes through.
The values from the problem's initial point and the slope we determined are substituted, and the result is:
$\left(y--4\right)=-\frac{2}{5}\left(x--7\right)$
$\left(y+4\right)=-\frac{2}{5}\left(x+7\right)$
We may also insert the values from the second point in the issue with the slope we calculated, resulting in:
$\left(y--6\right)=-\frac{2}{5}\left(x--2\right)$
$\left(y+6\right)=-\frac{2}{5}\left(x+2\right)$

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