Question

Please help with number 4. I dont understand and show work pls

Answer 1

Greetings!

Answer:

y =
`(-2)/(3) + 10`

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 =
`(-2)/(3)x + (1)/(3)`

So the gradient is
`(-2)/(3)`

Now as the points are given, (9 , 4)

The equation of the line so far is:

y = mx + c

4 =
`(-2)/(3)`(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 =
`(-2)/(3) + 10`

Hope this helps!