Answer:
[tex]y=2x-25[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)
Perpendicular lines always have slopes that are negative reciprocals, such as 2 and -1/2, 3/4 and -4/3.
1) Determine the slope (m)
[tex]y = \displaystyle -\frac{x}{2} - 2[/tex]
Rewrite the given line:
[tex]y = \displaystyle -\frac{1}{2}x - 2[/tex]
Now, we can clearly identify the slope to be [tex]\displaystyle-\frac{1}{2}[/tex]. Because perpendicular lines always have slopes that are negative reciprocals, the slope of the line we're currently solving for is therefore 2. Plug this into [tex]y=mx+b[/tex]:
[tex]y=2x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=2x+b[/tex]
Plug in the given point (9,-7) and solve for b:
[tex]-7=2(9)+b\\-7=18+b\\b=-25[/tex]
Therefore, the y-intercept is -25. Plug this back into [tex]y=2x+b[/tex]:
[tex]y=2x+(-25)\\y=2x-25[/tex]
I hope this helps!
