Question

What is the equation in slope-intercept form of the line that passes through the point (-4,7) and is perpendicular to

y = 4x + 15?

Answer 1

`y = - (1)/(4) x + 6`

Explanation:

To find the slope of the line that is perpendicular to

`y =4x + 15`

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

`4`

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

`4 * line \: 2 = - 1 \\ line \: 2 = ( - 1)/( 4)`

`\\ recall \: that \\ \: x = - 4 \: \: \: \: y = 7\: \: \: slope = - (1)/(4) \\ \\ y = mx + c \\ 7 = ( - (1)/(4)) - 4 + c \\ 7 = 1 + c`

`7 - 1= c \\ 6 = c \\ \\ therefore \: the \: equation \: of \: the \\ \: line \: is \\ y = - (1)/(4) x + 6`