Question

Lines l and M are parallel. Line l can be represented by the equation 3x+4y=8. If line m passes through the point (2, -5), which equation can be used to find the equation of line m?

Answer 1

Answer:

3y - 4x + 7 = 0

Step-by-step explanation

The equation of the line l in point slope form is expressed as;

y-y0 = m(x-x0)

Get the slope m of the known line

Given the line 3x+4y=8

4y = -3x+8

y = -3x/4 + 2

m = -3/4

The slope of the line m = -1/(-3/4) = 4/3

Substitute m = 4/3 and the point (2,-5) into the expression above;

y - (-5) = 4/3(x-2)

y+5 = 4/3 x + 8/3

Multiply through by 3;

3y + 15 = 4x + 8

3y-4x + 15 - 8 = 0

3y - 4x + 7 = 0

Hence the equation that can be used to find the equation of line m is 3y - 4x + 7 = 0