Question

What is the equation of the line that passes through `(-1,4)` and is perpendicular to the line that passes through the following points: `(-2,2),(5,-6)`?

Answer 1

`8y = 7 x + 39`

Explanation:

The slope m, of the line passing through `(x1,y1) & (x2,y2)` is

`m = (y2 - y1) / (x2 - x1)`
Thus the slope of the line passing through `(-2,2) & (5, -6)` is
`m = (-6 - 2) / ((5 - (-2))` = `-8 / 7`
Now if the slope of two lines which are perpendicular to each other are m and m', we have the relationship
`m * m' = -1`
So, in our problem, the slope, m2, of the first line = `-1 / (-8 / 7)`
= `7 / 8`
Let the equation of the line be `y = m2x + c`
Here, `m2 = 7 / 8`
So the equation is `y = 7 / 8 x + c`
It passes through the points, `(-1,4)`
Substituting the x and y values,
`4 = 7 / 8 * (-1) + c`
or `c = 4 + 7 / 8 = 39 / 8`
So the equation is
`y = 7 / 8 x + 39 / 8`
or `8 y = 7 x + 39`