How to Graph Linear Equations

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Line them up!

Things You'll Need

  • Calculators
  • Pencils
  • Erasers
  • Graph Papers
  • Rulers
  • Draw a pair of perpendicular lines. These are your axes (the plural of "axis"). Label the horizontal axis "x" and the vertical axis "y." Label several different values, both positive and negative, of x and y on both axes. This is the scale of the graph.

  • Remember that your equation should be in the form y = mx + b (if it is in a different form, solve for y in terms of x).

  • Draw a dot on the y axis at y = b. This is the y-intercept of the graph (the point at which the graph crosses the y-axis).

  • Choose a value for x other than 0 and mark this on the x-axis you've drawn. Lightly draw a vertical line that crosses this value of x on your x-axis.

  • Plug the x value you chose into your equation.

  • Solve for y. Lightly draw a horizontal line that crosses this value of y on your y-axis.

  • Make a dot where the two lines you just drew intersect.

  • Draw a straight line between this dot and the y-intercept. Extend this line in both directions to the edges of your graph. This line is the graph of your equation.

Tips & Warnings

  • The value "m" in y = mx + b is the slope of the graph. The slope is the ratio of vertical change to horizontal change between two points on the graph.
  • Example: The graph of the equation y = 2x + 5 has a slope of 2 and crosses the y-axis at y = 5.
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