Question

What is the equation for the line that is perpendicular to -7x + 8y = 6 through the point (1, –4)?

Answer 1

First writing the given equation in the form y = mx + c, we get:
8y = 7x + 6 which leads to:

`y= (7)/(8) x+(3)/(4)\ ................(1)`
The gradient of the line given by (1) is 7/8.
If the gradient of the perpendicular line is m we can write:

`(7)/(8)m=-1`
Therefore m = -(8/7).
The equation of the perpendicular line is:

`y=-(8)/(7)x+c`
Substituting the values given for the point on the perpendicular line and solving for the value of c, the required equation for the perpendicular line is:
`y=-(8)/(7)x-2(6)/(7)`
Writing the last equation in standard form and removing fractions, we get:
8x + 7y = -20