Question

Find the slope of the line which passes through the points (3,-2) and (3, 4).

Answer 1

Hint: The slope of the line is also known as gradient of a line is a number that gives the direction and steepness of the line. If we have two coordinates $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ then slope of a line passing through these points is as follows:
$slope=\left( \dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)$

Complete step-by-step answer:
We have been given the points (3, -2) and (3, 4) through which the line passes. Now we know that the slope of a line passing through the points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$ is given by as follows:
$slope=\left( \dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)$
So we have ${{x}_{1}}=3,{{y}_{1}}=-2,{{x}_{2}}=3,{{y}_{2}}=4$
$\Rightarrow slope=\left( \dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)=\dfrac{4-(-2)}{3-3}=\dfrac{6}{0}=\infty$ (infinity)
Since we know that if the slope is infinity means the line is perpendicular to the x-axis i.e. it makes an angle of ${{90}^{\circ }}$ with the x-axis.
Therefore, the required slope of the line is $\infty$ (infinity).

Note: Remember that if the slope of a line is equal to zero then it is parallel to the x-axis and if the slope tends to infinity then it is perpendicular to x-axis. Also, you can remember that if the x-coordinates of the two points through which line passes are same then it must be perpendicular to the x-axis and if y-coordinates of the two points through which line passes are same then it must be parallel to the x-axis.