Question

What is the equation of the line that passes through (2, -1) and is perpendicular to the line 1 whose equation is y=-1/2

x+4?

Answer 1

Explanation:

The point-slope form of the equation of a line is:

`y-y_1=m(x-x_1)`

So, the equation for this problem, let

`(x_1,y_1)=(2,-1)`

then,

`y-(-1)=m(x-2)\\y+1=m(x-2)`

If line (a) is perpendicular to line (b), then
`m_b` is equal to
`-(1)/(m_a)`. For this problem, let

`m_a=-(1)/(2)` and
`m_b=2`

So,

`y+1=(2)(x-2)\\y+1=2x-4\\(y+1)-1=(2x-4)-1\\y=2x-5`