How do you write the slope-intercept equation for the line that is perpendicular to the line #-5x + 2y = 16# and passes through the point #(5, 7)#?

1 Answer
Jun 30, 2017

Answer:

Use the fact that slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.

Substitute the point into the slope-intercept form to find the value of b.

Explanation:

Given: #-5x + 2y = 16#

Add 5x to both sides:

#2y = 5x + 16#

Divide both sides by 2:

#y = 5/2x+ 8#

We can observe that the slope of the line #5/2#. The slope of a line that is perpendicular is the negative reciprocal, #-2/5#

The slope-intercept form is:

#y = -2/5x+b#

To find the value of b, substitute in the point #(5,7)#:

#7= -2/5(5)+b#

#b = 9#

The equation is:

#y = -2/5x+9#