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

Answer:

$\frac{3}{2}$ will be the slope of the line perpendicular to xy.

Step-by-step explanation:

The equation of line xy is ( y-3 ) = $\frac{-2}{3}$ (x-4)

y = $\frac{-2}{3}$ ( x-4 ) + 3

y = $\frac{-2}{3}$ x + $\frac{8}{3}$ + 3

y = $\frac{-2}{3}$ x + $\frac{17}{3}$

So the line has slope = $\frac{-2}{3}$ and y-intercept = $\frac{17}{3}$.

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 = $\frac{-2}{3}$

mx ($\frac{-2}{3}$) = -1

m = ($\frac{3}{2}$)

$\frac{3}{2}$ will be the slope of the line perpendicular to xy.