Question

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

y = x-9 and passes through the point (7,9).

Answer 1

`y=-x+16`

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!