Question

What is the slope of the line that is perpendicular to the line that passes through (-2, 7) and (4, 9)? Type a numerical answer in the space provided.

Answer 1

Answer:

Therefore $m_{2}$ = -3.

Step-by-step explanation:

i) let us say the slope of the line passing through (-2,7) and (4,9) is $m_{1}$.

ii) to find the slope of the line passing through two points ($x_{1}$, $y_{1}$) and ($x_{2}$,$y_{2}$) we use the formula m = $\dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }$. Therefore we can say that  $m_{1}$ = $\dfrac{9 - 7}{4 - (-2)}$ = $\dfrac{1}{3}$.

iii) let us say the slope of the perpendicular line to the line  passing through (-2,7) and (4,9) is $m_{2}$

iv) from the formula for the slopes of a line and the line perpendicular to it which is given by $m_{1}$ × $m_{2}$ = -1, therefore $m_{2}$ = -1 ÷  $m_{1}$ = -3. Therefore $m_{2}$ = -3