Which equation represents a line which is perpendicular to the line 2x+y=-5

Question

1. y=−2x+6
2. y=21​x−7
3. y=−21​x+5
4. y=2x−2

Answer 1

2x+y=-5

Furst let put it in slope intercept to identify the slope. That will help us determine the line perpendicular to it

2x+y=-5

-2x. -2x

y= -5 -2x

y= -2x -5 so if y=mx +b the slope is -2

lines that are perpendicular have a product -1

or the negative reciprocal of original slope

So -2m=-1

So (-2/-2)m = (-1/-2)

m=1/2

so the line perpendicular to y=-2x-5 has a slope of 1/2

I don’t see any choices that satisfies it. But in the original problem look for choices where 1/2 is multiplied by x.

I hope this helped you get started! Have a great day!

Mrs. S

Answer 2

First, get the equation in a standard form----eg the "slope-intercept form", which is :

y = mx + b, where m is the slope, and b is the y intercept (where x = 0)

You are given: 2x+y=-5

rearrange to get: y = -2x - 5

So the slope is -2. For the perpendicular line, the slope is the negative inverse( in this case +1/2. None of the choices you listed has the right slope.

To help visualize things like this, you can use an online graphing tool, such as this one:

https://www.desmos.com/calculator