How to Graph Math Problems
Any algebraic equation can be represented by a line on a graph. Depending on the variables, the line can be straight or curved. Equations that create straight lines are called "linear" equations, and they involve two variables that are not raised to a power above one. Curved, or "nonlinear," equations can create many varieties of lines, such as parabolic, elliptic or hyperbolic. They occur when a variable in the equation is raised to a power above one. Nonlinear equations are more difficult to graph, but you can follow the same basic steps for both types.
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Instructions
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Draw a four-quadrant graph (two intersecting perpendicular lines) on a sheet of graph paper with a straight edge. Label the horizontal line as the x axis and the vertical line as the y axis, and mark off every two or five units. For small equations, you can simply count each square as one unit, but for larger equations, you may want to count them as five or 10.
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2
Write your equation in standard form (Ax + By = C) to determine if it is linear or not. Both the x and y variables will not be raised to a power above one if it is a linear equation.
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Find the y intercept by plugging in zero for x and solving the equation. For example, if you have the equation y = 1/2x + 2, and you put in zero for x, the y intercept is 2. This means that the line crosses the y axis at 2. Plot this point (0,2) on your graph -- two squares up on the y axis.
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4
Find the x intercept by putting zero in for y. Plot this point on the graph. In the equation y = 1/2x + 2, the x intercept is -4.
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Determine the slope of the line by looking at the number in front of the x variable. This will give you the rise over the run, or the number of units that you move up and over to get to the next point. In y = 1/2x + 2, the slope is 1/2, which means that every point is 1 unit up and 2 units to the right of the last one.
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Use the slope to plot two to five more points, or plug two or five more quantities into the equation to obtain more points to plot on the graph. For a linear equation, you probably only need three or four points to be able to draw a line through, but for a nonlinear equation, you should use about six or seven points to determine the shape of the graph.
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Use a straight edge to draw a line through the points of a linear equation. Draw a curved line connecting the points of a nonlinear equation.
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Tips & Warnings
Graphing calculators can help you find the shape of more difficult equations, but don't rely on it for every problem.
References
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