Question

Find an equation for a line perpendicular to y= 3x – 5 , with a y- intercept of -2

Answer 1

Answer:

Since the lines are Perpendicular..

The Product of their Gradients = -1

m'm"=-1

m' from y=3x - 5 is 3

3.m" = -1

m" = -1/3.

Since Intercept on y axis = -2...

That of x at that point is =0

y-y' = m"(x-x")

y-(-2) = -1/3( x - 0)

y+2 = -1/3(x)

Multiplying through by 3

3y + 6 = -x

3y + x = -6. This is your Equation

To verify this.

Let's turn it into the Intercept form which is

x/a + y/b = 1

To get 1 at the right hand side... Divide through by -6

3y/-6 + x/-6 = 1

y/-2 - x/6 = 1

You could see directly below y is its intercept and thats -2