Question

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

Answer 1

Answer:

$y=\frac{-1}{2} x+7$

Step-by-step 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 $\frac{-1}{2}$. Therefore, the slope of the perpendicular line is $\frac{-1}{2}$. So far, our equation looks like this:

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

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:

$y=\frac{-1}{2}x+b\\8=\frac{-1}{2}(-2)+b\\8=\frac{2}{2} +b\\8=1+b$

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:

$y=\frac{-1}{2} x+7$

I hope this helps!