Draw x and y axes. Plot the point (-2, -3) in quadrant III. The given slope is m = 5 which is equivalent to m = 5/1 (five divided by one). So the rise is 5 and the run is 1. Put your pencil on the point (-2, -3) and go over one and up five spaces. You end up at (-1, 2). Again go over 1 (the run) and up 5 (the rise). You end up at (0, 7), intercepting the y-axis 7 spaces above the origin. So b, the y-intercept, is 7.
The equation of a line represents many combinations of x and y, so we keep the letters to show that the graph is not just one point. We use the information about m = 5 (given) and b = 7 (we found it) to write the slope-intercept form y = 5x + 7.
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