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y = mx + b , great question
it depends on what you mean by slope. in math we define slope as rise over run, like when you draw a line on a plane, the slope is the "rise" or change in y divided by the "run" or change in x
Because Jesus says so? I think that's a much simpler perspective.
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this is because in the x y plane, traditionally x refers to horizontal movement, and y refers to vertical movement. so change in y over change in x gives us the "rise over run" which we previously defined as slope
so all you have to show is that m is change in y over change in x, and i will let you do that