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.
