xcopyv4n

2023-03-07

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

Nhluvukoj6m

Beginner2023-03-08Added 6 answers

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: $(y-{{y}_{1}})={m}(x-{{x}_{1}})$

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:

$(y-{-4})={-\frac{2}{5}}(x-{-7})$

$(y+{4})={-\frac{2}{5}}(x+{7})$

We may also insert the values from the second point in the issue with the slope we calculated, resulting in:

$(y-{-6})={-\frac{2}{5}}(x-{-2})$

$(y+{6})={-\frac{2}{5}}(x+{2})$

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: $(y-{{y}_{1}})={m}(x-{{x}_{1}})$

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:

$(y-{-4})={-\frac{2}{5}}(x-{-7})$

$(y+{4})={-\frac{2}{5}}(x+{7})$

We may also insert the values from the second point in the issue with the slope we calculated, resulting in:

$(y-{-6})={-\frac{2}{5}}(x-{-2})$

$(y+{6})={-\frac{2}{5}}(x+{2})$