Answer to Question #97488 in Analytic Geometry for Frank

Question

What is the equation of line which is pararrel to (3x-2y=5)and passes through the point (-2,-4)

Answer 1

1. We transform the general equation of a given line into a slope-intercept equation: 3x-2y=5; -2y=-3x+5; y=1.5x-2.5
2. The condition of parallel straight lines is k₁=k₂. Then we obtain y=1.5x+b.
3. A new line goes through the point (-2; -4):

-4=1.5*(-2)+b; -4=-3+b; b=-4+3; b=-1.

Consequently, the equation of the required straight line is y=1.5x-1, or 2y=3x-2, or 3x-2y=2.