Question

What is an equation in slope-intercept form of the line that is perpendicular to the graph of `y=2x+3` and passes through (3, -4)?

Answer 1

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

Explanation:

The slope of the line perpendicular to the graph of `y=2x+3` is `-1/2`. The perpendicular slope is the negative inverse of the original slope. The product of perpendicular slopes is `-1`, where:

`m_1m_2=-1`,

where:

`m_1` is the original slope `(2)` and `m_2` is the perpendicular slope.

`2m_2=-1`

Divide both sides by `2`.

`m_2=-1/2`

So we now have the slope and we have been given a point `(color(red)3,color(blue)(-4))`.

Find the point-slope form of the perpendicular line.

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

Plug in the known values.

`y-(color(blue)(-4))=-1/2(x-color(red)3)`

`y+4=-1/2(x-3)` `larr` point-slope form.

To convert the point-slope form to slope-intercept form, solve the point-slope form for `y`.

Slope-intercept form is: `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

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

`y+4=-1/2x+3/2`

Subtract `4` from both sides.j

`y=-1/2x+3/2-4`

Multiply `4` by `2/2` to get an equivalent fraction with `2` as the denominator.

`y=-1/2x+3/2-4xx2/2`

Simplify.

`y=-1/2x+3/2-8/2`

Simplify.

`y=-1/2x-5/2` `larr` perpendicular slope-intercept form

graph{(y-2x-3)(y+1/2x+5/2)=0 [-11.25, 11.25, -5.625, 5.625]}