Greetings!
Answer:
y = [tex]\frac{-2}{3} + 10[/tex]
Step-by-step explanation:
A line perpendicular to 2x = 1 - 3y has the same gradient (or slope). To find this we must isolate the y:
Move the -3y over to the other side making it a +3y:
3y + 2x = 1
Move the +2x over to the other side making it a -2x:
3y = -2x + 1
Divide everything by 3:
y = [tex]\frac{-2}{3}x + \frac{1}{3}[/tex]
So the gradient is [tex]\frac{-2}{3}[/tex]
Now as the points are given, (9 , 4)
The equation of the line so far is:
y = mx + c
4 = [tex]\frac{-2}{3}[/tex](9) + c
4 = -6 + c
Move the -6 over making it a +6:
4 + 6 = c
c = 10
So that means the full equation is:
y = [tex]\frac{-2}{3} + 10[/tex]
Hope this helps!
