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Using Slope and y-Intercept to Graph Lines (page 2 of 2)

Given a point on the line, you can use the slope to get to the "next" point by counting "so many up or down, and then so many over to the right". But how do you find your first point?

Take a look back at the graph of the first line and its equation: y = ( 2/3 )x 4 crossed the y-axis at y = 4, so the equation gave us the y-intercept. The second line did too: the graph of y = 2x + 3 crossed the y-axis at y = 3. This relationship always holds true: in y = mx + b, "b" gives the y-intercept, and "m" is the slope. We can use this fact to easily graph straight lines:

  • Graph the equation y = ( 3/5 ) x 2 from the slope and y-intercept.
  • From the equation, I know that the slope is m = 3/5, and that the line crosses the y-axis at
    y = 2. Copyright Elizabeth Stapel 2000-2011 All Rights Reserved


    I'll start by plotting this first point:


    y-intercept at y = -2


    From this point, I go up three and over five:


    'up two and over three' to get the second point


    Then I go up another three and over another five to get my third point:


    another 'up three and over five' to get the third point


    With three points, I can draw my line:


    graph of y = (3/5)x - 2

As a stylistic note, you should probably pencil in the "up and over", if you are using this technique for graphing your straight line. That way, your instructor will know where your points came from. Also, if you are going to graph this way (instead of doing a T-chart of points), you will need to do your graph very neatly. If your scale on your axis is at all inconsistent or if your axes are at all crooked, this method will not work!

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Cite this article as:

Stapel, Elizabeth. "Using Slope and y-Intercept to Graph Lines." Purplemath. Available from Accessed


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