Answer:
Step-by-step explanation:
Perpendicular lines are lines whose slopes are negative reciprocals of each other
To find the slope of the line we are given, we can rearrange the equation
[tex]4x - 5y = 4\\4x - 4 = 5y\\y = \frac{4}{5}(x) - \frac{4}{5}[/tex]
The slope of this line is [tex]\frac{4}{5}[/tex], so the slope of the other line is [tex]\frac{-5}{4}[/tex]
next, we can use the given point to find the equation [tex]y = mx +b[/tex]
we know m, we can solve for b
[tex]y = \frac{-5}{4}(x) + b\\-3 = \frac{-5}{4}(-2) + b\\-3 = \frac{5}{2} + b\\\frac{-6}{2} = \frac{5}{2} + b\\[/tex]
[tex]b = \frac{-11}{2}[/tex]
[tex]so,\\y = \frac{-5}{4}(x) - \frac{11}{2}[/tex]
