Question

which is the equation of a line that is parallel to 2x+5y=4 and goes through the point (5,-4)?

Answer 1

Given line is 2x+5y = 4

Subtract 2x from each side.

2x+5y-2x = 4-2x

5y = -2x+4

Divide to each side by  5

5y/5 = (-2/5)x+4/5

y = (-2/5)x+4/5

Slope say m1  = -2/5

Parallel lines have equal slope, so required line slope say m2 = -2/5.

And the point (x1,y1) = (5,-4).

Line equation is y+4 = -2/5(x-5)

5(y+4) = -2(x-5)

5y+20 = -2x+10

Subtract 20 From each side.

5y+20-20 = -2x+10-20

5y = -2x-10

Divide to each side by 5.

5y/5 = -2x/5-10/5

y = (-2/5)x-2

Required line equation is y = (-2/5)x-2.