A line is parallel to 2x-3y-=-2 and intersects the point (-3,-4). What is the equation of this parallel line?

Question

A line is parallel to 2x-3y-=-2 and intersects the point (-3,-4). What is the equation of this parallel line?

Answer 1

The equation  2x-3y=-2  is given in Standard Form (Ax+By=C).

 

If you convert (Ax+By=C) to slope-intercept form (y=mx+b) once and forever, you will find that the slope m = (-A/B).   Remember this.

 

This is very important:  all parallel lines have the same slope.  So, we know that the equation of the parallel line is (2x-3y=D) and we need the point (-3,-4) to determine D.

 

      2(-3)-3(-4)=D

        -6 + 12 = D

               6   = D

 

The parallel line has the equation:    2x-3y=6