Question

What is the slope, m, of the line that is perpendicular to the line y = 1/3x + 12 and passes

through the point (0,-5)?

Answer 1

The slope of the line is

`- 3`

The equation of the line is

`y = - 3x - 5`

Explanation:

To find the slope of the line that is perpendicular to

`y = (1)/(3) x + 12`

We have to first understand that if two lines are perpendicular it means that their slopes are the negative inverse of each other. Since the slope of the line that we know is

`(1)/(3)`

Then in order to find the slope of the other line we have to find its negative inverse

`(1)/(3) * line \: 2 = - 1 \\ line \: 2 = ( - 1)/( (1)/(3) ) \\ line \: 2 = - 1 * (3)/(1)`

`slope \: of \: line \: 2 = - 3 \\ \\ recall \: that: \: y = - 9 \: \ \: \: \: x = 1 \: \: \: m = -3 \\ y = mx + c \\ - 9 = ( - 3)1 = c \\ - 9 = - 3 + c \\ - 9 + 3 = c`

`- 6 = c \\ \\ therefore \: the \: equation \: of \: the \: \\ line \:is \\ y = - 3x - 6`