Assuming Slope in Slope-Intercept Form [Clarification]

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So when learning about slope-intercept form, the equation that was used looked like this: $y = 2x + 3$, it then displayed a graph where the slope was going up by two and across by one. What I need a bit of clarification on is that do we just assume that the slope is, in this case, $\frac{2}{1}$, or is there something else?