SOLUTION: Find the equation of the line that goes through the point (-5,6) and is perpendicular to the line 3x-5y=2. express in slope intercept form

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that goes through the point (-5,6) and is perpendicular to the line 3x-5y=2. express in slope intercept form       Log On


   

Question 748222: Find the equation of the line that goes through the point (-5,6) and is perpendicular to the line 3x-5y=2. express in slope intercept form
Answer by timvanswearingen(106) About Me  (Show Source):
You can put this solution on YOUR website!
First, find the slope of:
3x-5y+=+2
To do this, get the equation into slope-intercept form: y=mx+b
3x-5y+=+2
Subtract 3x from both sides:
-5y+=+-3x%2B2
Divide both sides by -5:
y+=+3%2F5%2Ax%2B2
So the slope of that line is 3/5.
When finding a perpendicular slope, just flip the slope and change the sign.
So the perpendicular slope will be:
-5%2F3
Now, you have a point the line will be going through: (-5,6) and the slope: -5/3
As its name suggests, you'll be using Point-Slope form now to find the equation of the line.
Y-Y1=M%28X-X1%29
Plug the x and y from your ordered pair in for X1 and Y1. Plug in -5/3 for m:
Y-6=-5%2F3%2A%28X-%28-5%29%29
Subtracting a negative is like adding a positive...
Y-6=-5%2F3%2A%28X%2B5%29
Now we just have to distribute, and get this into slope-intercept form (y=mx+b)
Y-6=-5%2F3%2AX-25%2F3%29%29
Add six to both sides:
Y-6%2B6=-5%2F3%2AX-25%2F3%2B6
Y=-5%2F3%2AX-25%2F3%2B18%2F3
Y=-5%2F3%2AX-7%2F3