Question

What is the equation of the line that is perpendicular to `y=-1/4x+1` and goes through `(0,-5)`?

Answer 1

The equation is `y=4x-5`

Explanation:

Two lines: `y=a_1x+b_1` and `y=a_2x+b_2` are:

• parallel if `a_1=a_2`

• perpendicular if `a_1*a_2=-1`

So we have to find `a_2` for which: `-1/4a_2=-1`

If we multiply this equation by `-4` we get: `a_2=4`, so the equation is:

`y=4x+b_2`

Now we have to find te value of `b_2` for which `f(0)=-5`

`f(0)=4*0+b_2=b_2`, so `b_2=-5`

Finally the formula is: `y=4x-5`