So firstly, an attribute of parallel lines is that they share the same slope. For this case, this new line will also have the same slope of -3/2.
Next, plug in (-4,-2) into the slope-intercept form of this equation to solve for b, or the y-intercept as such:
[tex] -2=-\frac{3}{2}*-4+b\\-2=6+b\\-8=b [/tex]
Putting our equation together, this new line is y = -3/2x - 8. You would graph this line so that it passes the y-axis at (0,-8) and everytime the x value increases by 2, the y-value decreases by 3.
