Math Help! (Pre-Calculus)?

Question

Find an equation of the line perpendicular to 5x + 3y = 12 and passing through the point (2, 3).

Please show how you'd get this and the answer! Thanks!

Answer 1

solve 5x + 3y = 12 for y

y=-(5/3)x+12=mx+12

m=-(5/3)

turn m upside down

m=-(3/5)

multiply m by -1

m=3/5 new slope for your perpendicular line

use point (2, 3) like this

since (y-3)/(x-2)=3/5 for your new perpendicular line

y-3=3/5(x-2)

y-3=3/5x-6/5

y=3/5x-6/5+3

answer

y=3/5x+1.8

Answer 2

a line perpendicular of another has a slope which is the negative reciprocal of the other... so first get this in y=mx+b form: y= -5/3 x + 4

the negative reciprocal of -5/3 is 3/5, so your new slope is going to be 3/5.... then you're given a point to make a new eq'n (2,3). the point slope formula is y-y1=m(x-x1) so you fill everything in y-3=3/5(x-2) then solve for y: y-3= 3/5x- 6/5 ---> y=3/5x-6/5+3 then combine those like terms (-6/5 and 3... i don't have my calculator) and you're done. =)