find an equation of the line that passes through 22 and is p

find an equation of the line that passes through (-2,2) and is parallel to the line passing through 3x-4y-22=0

given equation of line 3x-4y-22=0

4y=3x-22

y=(3/4)x -(22/4)

y=(3/4)x -(11/2)

slope of given line =3/4

we know slopes of parallel lines are equal

so slope of line parallel to 3x-4y-22=0 is 3/4

now

equation of parallel line with slope 3/4 passing through (-2,2) is

y-2=(3/4)(x-(-2))

y-2=(3/4)(x+2)

y-2=(3/4)x +(3/2)

y=(3/4)x +(3/2)+2

y=(3/4)x +(7/2)

therefore equation of the line that passes through (-2,2) and is parallel to the line passing through 3x-4y-22=0 is

y=(3/4)x +(7/2)