How can a change in the coefficient/constant affect the shape and location of the graph on the Cartesian plane? (For example, how do the graphs of y = 2x + 3 and y = 2x – 7 compare?)

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For the second one, I will assume you meant 2x^7. In y = 2x + 3, the y-intercept is 3, and for every one unit to the right on the graph, it moves up by two. Conversely, in y = 2x^7, the y-intercept is at 0, and the graph does not have a constant slope.