Question

Select the equation that contains the point (3, -9), and in which the graph of the line has a positive slope.

Answer 1

First thing to do is to solve each of these for y.  The first one is y=-4x-3; the second one is y=4x-21; the third one is y=4x+21; the fourth one is y=-4x+3.  From that you can tell the positive slopes are found in the second and third equations.  Those are the ones we will test now for the point (3, -9).  y=-9 and x=3, so let's fill in accordingly.  The second equation filled in is -9=4(3)-21.  Does the left side equal the right when we do the math?  -9=12-21 and -9=-9.  So the second one works.  Just for the sake of completion, let's do the same with the third: -9=4(3)+21.  Does -9=12+21?  Of course it doesn't.  Our equation is the second one above, y+9=4(x-3).