Question

How is slope related to right triangles on the coordinate plane?

Answer 1

slope is the change in y direction devided by the change in x direction to get the ratio of change per unit of x.
when you make a right triangle you mean that the horizontal and veritcals of that triangle are the x and y axi of the carthesian plane.
then the slope becomes the y side divided by the x side which is also how you calculate angles within a triangle right? say
then the angle of that corner is the tangent of the y side over the x side.