Question

Suppose that ax+by=c is the equation of a non-vertical line. Find the slope of this line.

Answer: Slope = -a/b

Suppose that the vector v⃗ =ai⃗ +bj⃗ is not vertical. Find the slope of this vector.
Answer: Slope = b/a

How would I use those two answers to answer the third part in the screenshot?

Answer 1

To address the hint: The slopes of perpendicular lines are negative reciprocals of one another.

The given line has slope
`-\frac ab`. Any line perpendicular to it will have slope
`-\frac1{-a/b} = \frac ba`, which is exactly the slope of the given vector.

Therefore a line perpendicular to the vector
`-9\,\vec\imath+6\,\vec\jmath`, which has slope
`\frac6{-9}=-\frac23`, would have slope
`-\frac1{-2/3} = \frac32`. The one passing through the point (-8, 7) then has equation

`y - 7 = \frac32 (x - (-8)) \implies -3x + 2y = 38`