Answer :
Answer:
y = 3x + 3
Step-by-step explanation:
Rules of Perpendicularity
[tex]y = mx + b[/tex] ⊥ [tex]y=-\frac{1}{m} x + b[/tex]
1 - Find your first equation
x + 3y = 272 | 1.1 - get y by itself by first subtracting x
-x -x
3y = -x + 272 | 1.2 - divide both sides by 3 and you've got it simplified
[tex]y = -\frac{1}{3}x + \frac{272}{3}[/tex]
That 272 over 3 looks pretty intimidating, however, all we really care about is that slope
2 - Use the slope to find the perpendicular
[tex]y = -\frac{1}{3}x+b[/tex] ⊥ [tex]y= -\frac{1}{-\frac {1}{3}}x+ b = \frac{3*1}{1} x+b = 3x+b[/tex]
[tex]y = -\frac{1}{3}x +b[/tex] ⊥ [tex]y = 3x + b[/tex]
3 - Use the perpendicular y = mx + b to find b when it passes through said point
y = 3x + b must pass through (1, 6) or (x, y)
Plug x and y in
6 = 3(1) + b
6 = 3 + b
-3 -3
3 = b
4.) Rewrite y=mx+b form with the found b
y = 3x + 3
Hope this helps,
- J.M.Jamon
Pennsylvania State University
Full-time B.S.CE. undergrad student