Question

Find the equation of the line that is perpendicular to the line

Answer 1

Answer:

$y=-x+16$

Step-by-step explanation:

Hi there!

What we need to know:

• 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 is 0)
• Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

y=x-9

Rewrite the equation

y=1x-9

Now, we can identify clearly that the slope of the line is 1. The negative reciprocal of 1 is -1, so therefore, the slope of a perpendicular line would be -1. Plug this into $y=mx+b$:

$y=-1x+b\\y=-x+b$

2) Determine the y-intercept (b)

$y=-x+b$

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

$9=-7+b$

Add 7 to both sides to isolate b

$9+7=-7+b+7\\16=b$

Therefore, the y-intercept is 16. Plug this back into $y=-x+b$:

$y=-x+16$

I hope this helps!