Write 2 equations of a line that passes through (-3,-4) one is perpendicular

Question

 

and the other one is parallel to y=4x+1 show work 

Answer 1

The equation is y=4x+1

The equation is in the form y=mx+c

Slope, m=4

Parallel equation slope is m1=m=4

Perpendicular equation slope is m2=(-1/m)=-1/4

To calculate parallel equation of line passes through (-3,-4) using below formulae

(y-y1)=m1(x-x1)

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

y+4=4(x+3)

y+4=4x+12

4x-y+8=0

Parallel equation is 4x-y+8=0

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To calculate perpendicular equation of line passes through (-3,-4) using below formulae

(y-y1)=m2(x-x1)

(y-(-4))=(-1/4)(x-(-3))

4(y+4)=-1(x+3)

4y+16=-x-3

x+4y+19=0

Perpendicular equation is x+4y+19=0