Question

Question #7356c

Answer 1

`-1/5x-6/5=y`

Explanation:

First, remember that the equation `-1/mx+b=y` is perpendicular to `mx+b=y`

First, write `5x-y=3` in the intercept form `y=mx+b`

`5x-y=3`
`5x=3+y`
`5x-3=y`

Since the slope is 5, the slope for the perpendicular line is `-1/5`

Since this line perpendicular to `5x-3=y` passes through (4,-2), we can use the formula `m(x-x_1)=y-y_1` to find the equation.

`-1/5(x-4)=y-(-2)` We need to make this into the form `y=mx+b`

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

`-x/5+4/5=y+2`
`-x/5+4/5-2=y`
`-x/5-6/5=y`
`-1/5x-6/5=y`
That is our answer! To prove this, simply graph these two points.

Answer 2

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

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

So the perpendicular line will have a slope of `-\frac{1}{5}`.

Now we can write the equation in point-slope form:

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

`\implies y+2=-\frac{1}{5}(x-4)`