Question

Find the equation of the line through (9,-7) that is perpendicular to the line y = -x/2 - 2

Answer 1

Answer:

$y=2x-25$

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: $y=mx+b$ 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)

$y = \displaystyle -\frac{x}{2} - 2$

Rewrite the given line:

$y = \displaystyle -\frac{1}{2}x - 2$

Now, we can clearly identify the slope to be $\displaystyle-\frac{1}{2}$. 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 $y=mx+b$:

$y=2x+b$

2) Determine the y-intercept (b)

$y=2x+b$

Plug in the given point (9,-7) and solve for b:

$-7=2(9)+b\\-7=18+b\\b=-25$

Therefore, the y-intercept is -25. Plug this back into $y=2x+b$:

$y=2x+(-25)\\y=2x-25$

I hope this helps!