Answer:
[tex]y = \frac{4}{3} x +1[/tex]
Step-by-step explanation:
1: find the perpendicular gradient - this is the negative reciprocal of the original gradient:
[tex]y=\frac{-3}{4}x+ 2 \\y=\frac{4}{3} x+c[/tex]
2: Substitute in the coordinate to find the value of c:
[tex]y=\frac{4}{3}x +c\\5 = \frac{4}{3} (3) + c\\5 = 4+c\\c=1[/tex]
3: Put it all together:
[tex]y=\frac{4}{3}x+1[/tex]
