Question

given the line 5x-4y=8, find the equation of a line parallel to this line that passes through the point (3, -2)


thank you

Answer 1

also part B

find the equation of a line perpendicular to this line that passes through the point (3, -2)

thanks

Answer 2

looks like you need to review slopes
parallel lines have equal slopes
perpendicular lines with slopes m1 and m2 have m1 * m2 = -1

(A) 5x-4y=8 has slope 5/4
Now you have a point and a slope, so use the point-slope form of the line
y+2 = 5/4 (x-3)

(B) the perpendicular line has slope -4/5
y+2 = -4/5 (x-3)

rearrange as you like.

Or, just modify the equation they gave you. You want a parallel line, so
5x-4y=C
it passes through (3,-2), so
5(3) - 4(-2) = C
will do the job.

to get the line perpendicular to 5x-4y=8 use
4x+5y=C
4(3) + 5(-2) = C