Question

Write an equation that passes through (4,-3) and is perpendicular to y=-2x-4

Answer 1

The point is (4,-3) and is perpendicular to y=-2x-4.

The slope is given , m=-2.

For the perpendicular line, the slope is

`m_1* m_2=-1`
`m_1*-2=-1`
`m_1=(1)/(2)`

Now, then the general equation is

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

Substitute the values.

`y-(-3)=(1)/(2)(x-4)`
`y+3=(1)/(2)(x-4)`
`y=(1)/(2)x-(4)/(2)-3`
`y=(1)/(2)x-2-3`
`y=(1)/(2)x-5`

Hence the equation is determined as

`y=(1)/(2)x-5`