the line x=0,y=2x-5,and y=mx+9 for a right triangle. find two possible values of m

Question

the line x=0,y=2x-5,and y=mx+9 for a right triangle. find two possible values of m

please show work Q_Q

Answer 1

It helps if you sketch out this problem. When you draw all three lines you'll see a triangle with one side on the y-axis (x=0) and two intersecting lines, one that starts at (0,-5) represented by y=2x -5, and the other that starts at (0,9) representing y = mx + 9.

We have to use the fact that this is a right triangle, which means y = mx+9 would have to represent a horizontal line with m=0 for the slope, so y = 9.

I don't believe that there is another way to draw this right triangle, as the y-intercept is fixed at (0,9) for the y = mx + 9.

Answer 2

mx+9 must be perpendicular to one of the other two lines to form a right triangle

m = 0 gives a horizontal line (perpendicular to x=0)

m=-(1/2) gives a line perpendicular to a line with slope 2.