The line that is perpendicular to [tex]y = \dfrac{4}{5}x+23[/tex] and passes through (-40,20) is [tex]y = \dfrac{-5}{4}x-30[/tex].
We have to determine, which equation represents the line that is perpendicular to y = 4/5x+23 and passes through (-40,20).
According to the question,
Equation of line; [tex]y = \dfrac{4}{5}x+23[/tex]
To determine the equation perpendicular line passes through the given points determined in the following steps given below.
[tex]m = \dfrac{4}{5}[/tex]
[tex]m = \dfrac{-5}{4}[/tex]
[tex]y = mx + b\\\\20 = \dfrac{-5}{4} \times -40 + b\\\\20 = -5 \times -10 +b \\\\20 = 50 + b \\\\b = 20-50\\\\b = -30[/tex]
[tex]y = mx + b\\\\y = \dfrac{-5}{4}x-30[/tex]
Hence, The line that is perpendicular to [tex]y = \dfrac{4}{5}x+23[/tex] and passes through (-40,20) is [tex]y = \dfrac{-5}{4}x-30[/tex].
To know more about the Straight line click the link given below.
https://brainly.com/question/1249
