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

Therefore
`m_(2)` = -3.

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 =
`(y_(2) - y_(1) )/(x_(2) - x_(1) )`. Therefore we can say that
`m_(1)` =
`(9 - 7)/(4 - (-2))` =
`(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