Answer:
[tex]y=\frac{-1}{2} x+7[/tex]
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 [tex]\frac{-1}{2}[/tex]. Therefore, the slope of the perpendicular line is [tex]\frac{-1}{2}[/tex]. So far, our equation looks like this:
[tex]y=\frac{-1}{2}x+b[/tex]
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:
[tex]y=\frac{-1}{2}x+b\\8=\frac{-1}{2}(-2)+b\\8=\frac{2}{2} +b\\8=1+b[/tex]
Subtract both sides by 1 to isolate b
[tex]8-1=1+b-1\\7=b[/tex]
Therefore, the y-intercept of this line is 7.
After plugging both the slope and the y-intercept into y=mx+b, we get:
[tex]y=\frac{-1}{2} x+7[/tex]
I hope this helps!
