How to find an equation of the line containing the given pair of points(-7, -4)...

First, we need to determine the slope of the line running through the two points. The slope can be found by using the formula: ${\displaystyle m=\frac{y_2-y_1}{x_2-x_1}}$
Where ${\displaystyle m}$ is the slope and (${\displaystyle x_1,y_1}$) and (${\displaystyle x_2,y_2}$) are the two points on the line.
The result of substituting the values from the problem's points is:
${\displaystyle m=\frac{-6--4}{-2--7}=\frac{-6+4}{-2+7}=\frac{-2}{5}=-\frac{2}{5}}$
We can now use the point-slope formula to write and equation for the line. The point-slope formula states: ${\displaystyle (y-y_1)=m(x-x_1)}$
Where ${\displaystyle m}$ is the slope and ${\displaystyle \left(\begin{array}{cc}{x}_1& y_1\end{array}\right)}$ 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:
${\displaystyle (y--4)=-\frac{2}{5}(x--7)}$
${\displaystyle (y+4)=-\frac{2}{5}(x+7)}$
We may also insert the values from the second point in the issue with the slope we calculated, resulting in:
${\displaystyle (y--6)=-\frac{2}{5}(x--2)}$
${\displaystyle (y+6)=-\frac{2}{5}(x+2)}$