Question

Find the slope of the line parallel to the line joining the points $(-4,3)$ and $(2,5)$.

Answer 1

We know that the slope of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, the given points are $(-4,3)$ and $(2,5)$, therefore, the slope of the line is:

$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{5-3}{2-(-4)}=\frac{2}{6}=\frac{1}{3}$

We also know that if the slope of the two lines are equal that is $m_1=m_2$, then the lines are parallel, therefore, the slope $m_2$ of the line parallel to the given line is:

$m_1=m_2=\frac{1}{3}$

Hence, the slope of the line parallel to the given line is$\frac{1}{3}$.