Question

What is the equation of the line that is perpendicular to y = −2x + 5 through the point (-4, -5)

Answer 1

Explanation:

m1=-2

m1m2=-1

-2m2=-1

m2=1/2

y+5/x+4=1/2

so 2y+10=x+4

2y-x=-6

Answer 2

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

Explanation:

Hi there!

We are given the equation y=-2x+5 and we want to find the equation of the line that is perpendicular to that line, and pass through the point (-4, -5)

Perpendicular lines have slopes that multiply to get -1.

So to find the slope of the perpendicular line: use the formula
`m_1*m_2=-1`, where
`m_1=-2`

Substitute:

-2m=-1

Divide both sides by -2

m=
`(1)/(2)`

Here's the equation of the line so far, as we know it, written in slope-intercept form (y=mx+b, where m is the slope and b is the y intercept):

`y=(1)/(2)x+b`

We need to find b.

Because we know the line passes through the point (-4, -5), we can use it to help solve for b.

Substitute -4 as x and -5 as y

`-5=(1)/(2)(-4)+b`

Multiply:

-5=-2+b

Add 2 to both sides

-3=b

Substitute -3 as b:

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

Hope this helps!