Question

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

Answer 1

`y=2x-25`

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 -(x)/(2) - 2`

Rewrite the given line:

`y = \displaystyle -(1)/(2)x - 2`

Now, we can clearly identify the slope to be
`\displaystyle-(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!