How to Graph Linear Equations in College Algebra

Linear equations are used to determine the relationship between two variables. A graphical representation of your linear equations aids in easily understanding the relationships. When having multiple linear equations, you can plot it on the same graph to compare different scenarios. It provides the reader a clear picture of trends and historical references, thereby helping your reader make informed decisions on which approach would be best to get the best output.

Things You'll Need

  • Pencil
  • Graph paper
  • Ruler
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Instructions

  1. Draw the Graph

    • 1

      Draw a graph. Use a pencil and a ruler to make two straight lines, one vertical and one horizontal that intersect each other.

    • 2

      Label the horizontal axis "x" and the vertical axis "y."

    • 3

      Label the point your axes intersect "0." This is your origin. Label positive points of equal increments on the vertical axis above the origin and on the horizontal axis to the right of the origin. Label negative points of equal increments on the vertical axis below the origin and on the horizontal axis to the left of the origin. This is your scale.

    Plot Your Linear Equations

    • 4

      Gather coordinates. For example, the linear equation is: y = 2x + 3. This takes the form "y = mx + b" where "m" = slope and "b" = y-intercept. Select values of x to get outputs of y. For example, substitute the x-values -1, 0 and 1 each into your linear equation. The corresponding y-values = 1, 3 and 5, respectively. Therefore, the three coordinates are (-1,1), (0,3) and (1, 5). You can use any coordinates for this exercise.

    • 5

      Plot the coordinates on your graph by lightly drawing a small point at that coordinate. For example, for coordinate (-1,1), locate "-1" on your x-axis and "1" on your y-axis. Make a small point at that coordinate. Do the same for the other coordinates.

    • 6

      Use the ruler to draw a straight line joining the coordinates. Extend the line in both directions to the edge of your graph.

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