Respuesta :
Answer:
Parallel line:
[tex]y=-\frac{4}{5}x+\frac{9}{5}[/tex]
Perpendicular line:
[tex]y=\frac{5}{4}x-\frac{1}{2}[/tex]
Step-by-step explanation:
we are given equation 4x+5y=19
Firstly, we will solve for y
[tex]4x+5y=19[/tex]
we can change it into y=mx+b form
[tex]5y=-4x+19[/tex]
[tex]y=-\frac{4}{5}x+\frac{19}{5}[/tex]
so,
[tex]m=-\frac{4}{5}[/tex]
Parallel line:
we know that slope of two parallel lines are always same
so,
[tex]m'=-\frac{4}{5}[/tex]
Let's assume parallel line passes through (1,1)
now, we can find equation of line
[tex]y-y_1=m'(x-x_1)[/tex]
we can plug values
[tex]y-1=-\frac{4}{5}(x-1)[/tex]
now, we can solve for y
[tex]y=-\frac{4}{5}x+\frac{9}{5}[/tex]
Perpendicular line:
we know that slope of perpendicular line is -1/m
so, we get slope as
[tex]m'=\frac{5}{4}[/tex]
Let's assume perpendicular line passes through (2,2)
now, we can find equation of line
[tex]y-y_1=m'(x-x_1)[/tex]
we can plug values
[tex]y-2=\frac{5}{4}(x-2)[/tex]
now, we can solve for y
[tex]y=\frac{5}{4}x-\frac{1}{2}[/tex]
