Question

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

Answer 1

Step-by-step 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

Answer:

$y=\frac{1}{2}x-3$

Step-by-step 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=$\frac{1}{2}$

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):

$y=\frac{1}{2}x+b$

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

$-5=\frac{1}{2}(-4)+b$

Multiply:

-5=-2+b

Add 2 to both sides

-3=b

Substitute -3 as b:

y=$\frac{1}{2}x-3$

Hope this helps!