SOLUTION: I need help. Find the equation of a line that is perpendicular to y=-x + 3 and passes through the point(-1, 2).

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I need help. Find the equation of a line that is perpendicular to y=-x + 3 and passes through the point(-1, 2).      Log On


   

Question 332067: I need help. Find the equation of a line that is perpendicular to y=-x + 3 and passes through the point(-1, 2).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-x%2B3 has a slope m=-1 and a y-intercept b=3.


Now to find the slope of the perpendicular line, simply flip the slope m=-1 to get m=-1%2F1. Now change the sign to get m=1. So the perpendicular slope is m=1.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=1 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-2=1%28x--1%29 Plug in m=1, x%5B1%5D=-1, and y%5B1%5D=2


y-2=1%28x%2B1%29 Rewrite x--1 as x%2B1


y-2=1x%2B1%281%29 Distribute


y-2=1x%2B1 Multiply


y=1x%2B1%2B2 Add 2 to both sides.


y=1x%2B3 Combine like terms.


y=x%2B3 Simplify.


So the equation of the line perpendicular to y=-x%2B3 that goes through the point is y=x%2B3.


Here's a graph to visually verify our answer:


Graph of the original equation y=-x%2B3 (red) and the perpendicular line y=x%2B3 (green) through the point .