Determine an equation of the line which passes through (2,3) and perpendicular to a line with x intercept 4 and y intercept 5.

Question

Determine an equation of the line which passes through (2,3) and perpendicular to a line with x intercept 4 and y intercept 5.

Answer 1

first find equation of line y₁, find the slope using the information about the intercepts

x intercept = (4,0) and y intercept=(0, 5)

m₁=(5-0)/(0-4)=-5/4

the equation of y₁

y_{1= (-5x)/4+5}

now find y₂ ,

m₂=-1/m₁ the negative reciprocal

m₂=4/5

y-y₁=m(x-x₁)

y-3=4/5(x-2)

find an equation of the line which passes through (2,3) and perpendicular to a line with x intercept 4 and y intercept 5 by solving the above equation for "y"