Question

Find an equation of the line that bisects the acute angles formed by the lines with equations 2x+y-5=0 and 3x-2y+6=0.

Answer 1

okay. i was on my phone answering some questions, but this one need serious work so i went to my laptop. Tell me what course this is because we can solve this in geometry as well as Algebra

Answer 2

This is for my pre-calc class. @Will.H

Answer 3

okay. if you graph those 2 equations you'll get the following

Answer 4

so am guessing the equation we will form will have a slope equal to zero

Answer 5

I think the slope would have to be the average of the slope of the two lines.

Answer 6

basically we need to form an equation that passes through the intersection point

Answer 7

you just need to add the equations together. combine like terms and you'll get a new equation
see the attachment below

Answer 8

Hope that helps.

Answer 9

@Will.H that clearly does not bisect the angles.

Answer 10

uh. i thought the question asks to bisect the 2 equations only. sorry. let me check back

Answer 11

Anyway @Kpoprocks21 you should have some input or work or something...

Answer 12

@agent0smith am waiting for you to solve this tho. your a legend :)

Answer 13

here's what i know about bisectors, and you should work on this not just wait someone to solve it.
Algebraically
The equations of the bisectors of the angles between the lines
ax + by + c = 0 and a'x + b'y + c' = 0 (ab' ≠ a'b) are:
(ax + by + c) / √(a^2 + b^2) = ± (a'x + b'y + c') / √(a'^2 + b'^2).

Hope that helps