SOLUTION: Find an equation of the line in function notation through (2, -6) and perpendicular to -3x - 5y = 2.

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Question 186131: Find an equation of the line in function notation through (2, -6) and perpendicular to -3x - 5y = 2.

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!

The Slope=m%5B1%5D of a line -3x-5y=2 is the negative reciprocal--->m%5B2%5D=-1%2Fm%5B1%5D of the Slope=m%5B2%5D of the line that passes thru (2,-6). (*perpendicular lines remember?)
Given line Eqn via Slope-Intercept Form, y=mx%2Bb
5y=-3x-2---->cross%285%29y%2Fcross%285%29=%28-3x-2%29%2F5
y=highlight%28%28-3%2F5%29%29x-%282%2F5%29--> Slope=m%5B1%5D=-3%2F5
Then,
m%5B2%5D=-1%2F%28-3%2F5%29=-1%2A%285%2F-3%29=5%2F3
So therfore thru point (2,-6): (Slope-Intercept Form)
-6=%285%2F3%292%2Bb---->b=-6-10%2F3=%28-18-10%29%2F3=-28%2F3, Y-intercept
It follows---->highlight%28y=%285%2F3%29x-28%2F3%29%29, ANSWER
Let Fy=0---->0=%285%2F3%29x-28%2F3---->%285%2F3%29x=28%2F3
cross%285%2F3%29x%2Fcross%285%2F3%29=%2828%2F3%29%2F%285%2F3%29=%2828%2Fcross%283%29%29%28cross%283%29%2F5%29
x=28%2F5
Let Fx=0---->y=%285%2F3%29%280%29-28%2F3}---->y=-28%2F3
Let's plot the points:
drawing%28400%2C400%2C-4%2C10%2C-10%2C5%2Cgrid%281%29%2Cgraph%28400%2C400%2C-4%2C10%2C-10%2C5%2C%285%2F3%29x-%2828%2F3%29%29%2Ccircle%2828%2F5%2C0%2C.10%29%2Ccircle%280%2C-28%2F3%2C.10%29%2Cblue%28circle%282%2C-6%2C.16%29%29%29--->Line Eqn y=%285%2F3%29x-28%2F3%29----> Perpendicular to y=%28-3%2F5%29x-%282%2F5%29->GREEN Line:drawing%28400%2C400%2C-4%2C10%2C-10%2C5%2Cgrid%281%29%2Cgraph%28400%2C400%2C-4%2C10%2C-10%2C5%2C%285%2F3%29x-%2828%2F3%29%2C%28-3%2F5%29x-%282%2F5%29%29%2Ccircle%2828%2F5%2C0%2C.10%29%2Ccircle%280%2C-28%2F3%2C.10%29%2Cblue%28circle%282%2C-6%2C.16%29%29%29%29
Thank you,
Jojo