Question

Determine the equation of the line that passes through the point (7, -23)and is perpendicular to the line y=1/3x-6Enter your answer in slope-intercept form.

Answer 1

We have a line y = 1/3x -6

We want a line that is perpendicular to this line

Perpendicular lines have slopes that multiply to -1

1/3 * m = -1

3 * 1/3 *m = -1 * 3

m = -3

The slope of the perpendicular line is -3

y = mx+b where m is the slope and b is the y intercept

y = -3x+b

We have a point on the line ( 7 ,-23)

Substitute this point into the equation

-23 = -3(7)+b

-23 = -21+b

Add 21 to each side

-23+21 = -21+21+b

-2 = b

y = -3x-2

In slope intercept form, the line perpendicular passing through (7,-23) is

y = -3x-2