Question

The equation of line XY is (y-3)= -2/3(x-4).What is the slope of a line perpendicular to XY?

a) -2

b) 3

c) -2/3

d) 2/3

Answer 1

Equation of the line: (y - 3) = -2/3 (x - 4)
Compare it with: (y - y1) = m(x - x1)
Then, m = -2/3

Now, we know perpendicular line must have equal & opposite slope so:
It would be: 3/2

In short, Your Answer would be 3/2
[ Please check the options ]

Hope this helps!

Answer 2

`(3)/(2)` will be the slope of the line perpendicular to xy.

Explanation:

The equation of line xy is ( y-3 ) =
`(-2)/(3)` (x-4)

y =
`(-2)/(3)` ( x-4 ) + 3

y =
`(-2)/(3)` x +
`(8)/(3)` + 3

y =
`(-2)/(3)` x +
`(17)/(3)`

So the line has slope =
`(-2)/(3)` and y-intercept =
`(17)/(3)`.

Let m is the slope of a line perpendicular to line xy.

We know that for perpendicular lines having slopes m₁ and m₂

m₁ × m₂ = -1

Therefore, for m₁ = m and m₂ =
`(-2)/(3)`

mx (
`(-2)/(3)`) = -1

m = (
`(3)/(2)`)

`(3)/(2)` will be the slope of the line perpendicular to xy.