What is the equation of the line that is perpendicular to the first line and passes through the point (5, -4)

Question

A line passes through the point (-2,-4), and its y-intercept is (0,-6)

Answer 1

-4 = -2m - 6

2m = -2

m = -1

 

-4 = 1(5) + b

-4 = 5 + b

b = -9

 

y = x - 9

Answer 2

Step 1: You must first find the slope of the original line going through (-2,-4) and (0,-6)

Remember to find the slope of a line is m=(y₂-y₁)/(x₂-x₁), so the slope of this line is (-6-(-4))/(0-(-2))=(-6+4)/(0+2).

Since a negative times a negative gives you positive. So, that gives us m=-2/2=-1

 

Step 2: Remember now that perpendicular lines have negative reciprocal slopes(m1=-1/m₂). The negative reciprocal of -1 is 1. So, the slope of the perpendicular line is 1.

 

Step 3: Find the equation that goes through that line. You have two options, you can use slope-intercept form(y=mx+b), or you may use the point-slope form(y-y₁)=m(x₂-x₁) 

 

Since the perpendicular line is supposed to go through the point (5,-4) that will be our (x,y) coordinate or (x₁,y₁)

 

slope-intercept form: -4=(1)(5)+b, now our job is to solve for b, which gives us b=-9, therefore the equation of the line is y=x-9.

 

Point-Slope form: y-(-4)=(1)(x-5), which gives us y+4=x-5, technically this is done, but if it has to be in slope-intercept form, then just subtract "4" from both sides of the equation. which will give you y=x-9 also.