Answer:
slope of parallel line and perpendicular line are 5 and -1/5 espectively
equation of parallel and perpendicular line are y = 5x + 22 [tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex] respectively
Step-by-step explanation:
y = 5x - 4 is in the form
y = mx + c
where m is the slope of the line and c is the y intercept of thr line
therefore slope of the line = 5 and y intercept = -4
when an another line is parallel to the given line then the slope of both the lines are equal
therefore the slope the parallel line = 5
equation of a line passing through a given point [tex](x_{1} ,y_{1})[/tex] with slope m is given by [tex]y-y_{1} = m(x-x_{1} )[/tex]
given [tex](x_{1} ,y_{1})[/tex]= (-4,2)
therefore equation of line y-2 = 5(x+4)
therefore y = 2+ 5x+20
y = 5x + 22is the eqaution of required line.
when two lines are perpendiculer then
[tex]m_{1} m_{2}=-1[/tex]
where [tex]m_{1} and m_{2}[/tex] are slope of the lines therefore
m×5=-1
therefore m= [tex]\frac{-1}{5}[/tex]
therefore eqaution of line passing through (-4,2) and with slope m= [tex]\frac{-1}{5}[/tex] is given by [tex]y - 2= \frac{-1}{5} (x+4)[/tex]
[tex]y= \frac{-1}{5} x+\frac{6}{5}[/tex]
