When would you use slope and Y-intercept?

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you need them both when graphing and when writing an equation of a graphed line

You might use it to create a graph of a line. For example, you might be given a slope of 2 and a y intercept of 4 and be asked to draw the graph. You, of course, would draw a line that passes through the point 0, 2 (y-intercept) and that rises two units for every one unit it moves to the right.