The Algebra of Lines:

Graphing a Line Using the Slope and Y-Intercept

In this lesson, we learn how to graph our line using the y-intercept and the slope. First, we know that the y-intercept (b) is on the y-axis, so we graph that point. Next, we use the slope to find a second point in relation to that intercept. The following video will show you how this is done with two examples.

Video Source (05:37 mins) | Transcript

Steps for graphing an equation using the slope and y-intercept:

  1. Find the y-intercept (b when the equation is y = mx + b).
  2. Plot the y-intercept, the point will be (0, b).
  3. Find the slope (m when the equation is y = mx + b).
  4. Make a single step, using the rise and run from the slope (make sure you go up to the right if it’s positive and down to the right if it’s negative).
  5. Connect those two points with your line.

Additional Resources

Practice Problems

  1. Plot the line \({\text{y}}=-3{\text{x}}+2\) starting with the y-intercept and then using the slope.
  2. Plot the line \({\text{y}}=\frac{1}{2}{\text{x}}-3\) starting with the y-intercept and then using the slope.
  3. Plot the line \({\text{y}}=-\frac{3}{5}{\text{x}}+1\) starting with the y-intercept and then using the slope.
  4. Plot the line \({\text{y}}=2{\text{x}}+3\) starting with the y-intercept and then using the slope.
  5. Plot the line \({\text{y}}=-{\text{x}}-4\) starting with the y-intercept and then using the slope.
  6. Plot the line \({\text{y}}=\frac{4}{5}{\text{x}}+4\) starting with the y-intercept and then using the slope.

Solutions

  1. Note: The graph you create may look slightly different depending on the spacing you choose for your x and y-axis. The correct graph should still have the same direction of slope and the x and y-intercepts should be the same.
    This is a picture of a coordinate plane. It has the graph of a line passing through the points (-1,5), (0,2), (1,-1) and (2,-4). (Written Solution)

  2. Note: The graph you create may look slightly different depending on the spacing you choose for your x and y-axis. The correct graph should still have the same direction of slope and the x and y-intercepts should be the same.
    This is a picture of a coordinate plane. It has the graph of a line passing through the points (-4,-5),(-3, -4.5), (-2, -4), (-1,-3.5), (0, -3), (1,-2.5), (2, -2), (3, -1.5), (4, -1), (5, -0.5), (6, 0), (7, 0.5) and (8,1).

  3. Note: The graph you create may look slightly different depending on the spacing you choose for your x and y-axis. The correct graph should still have the same direction of slope and the x and y-intercepts should be the same.
    This is a picture of a coordinate plane. It has the graph of a line passing through the points (-6, 4.6),(-5, 4), (-4, 3.4), (-3, 2.8), (-2, 2.2), (-1, 1.6), (0, 1), (1, 0.4), (2, -0.2), (3, -0.8), (4, -1.4), (5, -2), (6, -2.6), (7, -3.2) and (8, -3.8).

  4. Note: Your graph may look a little different depending on the spacing you choose for your x and y-axis. Notice in this graph the hash marks for the x-axis are farther apart than the hash marks for the y-axis. This artificially makes the graph look less steep than it is if the hash marks are the same distance apart. However, sometimes this is helpful in order to better fit the data into the graph.
    This is a picture of a coordinate plane. It has the graph of a line passing through the points (3,9), (2,7), (1,5), (0,3), (-1,1), (-2,-1), (-3,-3), (-4,-5), (-5,-7) and (-6,-9).

  5. Note: In this graph, the spacing of the hash marks on the x and y-axis are spaced almost identically.
    This is a picture of a coordinate plane. It has the graph of a line passing through the points (3,-7), (2,-6), (1,-5), (0,-4), (-1,-3), (-2,-2), (-3,-1), (-4,0), (-5,1), (-6,2), (-7,3), (-8,4) and (-9,5). (Written Solution)

  6. This is a picture of a coordinate plane. It has the graph of a line passing through the points (3,6.4), (2,5.6), (1,4.8), (0,4), (-1,3.2), (-2,2.4), (-3,1.6), (-4,0.8), (-5,0), (-6,-0.8), (-7,-1.6), (-8,-2.4) and (-9,-3.2).