Question

Passing through (-2, 8) and PERPENDICULAR to y = 2x + 5

Write a linear equation with the given information. Please hurry! It’s due in 10 minutes!

Answer 1

`y=(-1)/(2) x+7`

Explanation:

The slope of a perpendicular line will always be the NEGATIVE RECIPROCAL of the slope of the original line.

y=2x+5

Because this equation is organized in slope-intercept form, y=mx+b, we can identify the slope of the original line is 2. The negative reciprocal of 2 is
`(-1)/(2)`. Therefore, the slope of the perpendicular line is
`(-1)/(2)`. So far, our equation looks like this:

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

Now, we must solve for b, the y-intercept of this line. To do that, we can plug in the given point (-2,8) and solve for b:

`y=(-1)/(2)x+b\\8=(-1)/(2)(-2)+b\\8=(2)/(2) +b\\8=1+b`

Subtract both sides by 1 to isolate b

`8-1=1+b-1\\7=b`

Therefore, the y-intercept of this line is 7.

After plugging both the slope and the y-intercept into y=mx+b, we get:

`y=(-1)/(2) x+7`

I hope this helps!