How to graph a straight line

Every step

1. 1

   Rewrite the equation as y = mx + b

   Use −2x + y = 1 as the running example. Add 2x to both sides to get y = 2x + 1. Here m = 2 is the slope and b = 1 is the vertical intercept. Use the same equation for every point you plot. A vertical line such as x = 3 needs a different approach.

   CHECKPOINT · You have y = 2x + 1 and know its slope and intercept.
2. 2

   Plot the y-intercept

   Locate the y-intercept (b) on the vertical axis. For y = 2x + 1, b = 1. Put a point at (0,1) on the graph.

   CHECKPOINT · Y-intercept marked (e.g., (0,1)).
3. 3

   Use the slope to find another point

   The slope (m) is rise over run. For y = 2x + 1, slope is 2, so up 2, right 1 from (0,1) lands at (1,3). Mark (1,3) on the graph.

   CHECKPOINT · Second point marked using slope (e.g., (1,3)).
4. 4

   Plot a third point for accuracy

   From (1,3), go up 2, right 1 to (2,5), and mark (2,5). Alternatively, go down 2, left 1 from the y-intercept for a backwards point.

   CHECKPOINT · At least three collinear points plotted.
5. 5

   Draw the straight line

   Using a ruler, draw a solid line through the three points, continuing it across the graph. Label the line with its equation for clarity.

   CHECKPOINT · Line extends through all plotted points and is labeled.