Graphing Linear Equations

Plotting points method:
1. Solve the equation for y (write in y=mx+b form)
2. Find at least 3 ordered pair solutions:
            a. Choose a value for x
            b. Substitute that value for x in the equation.
            c. Calculate the value for y.
            d. The ordered pair solution is in the form:
              (the x value you chose , the y value you calculated)
            e. repeat steps a – d   until you have at least 3 ordered pairs.
3. Graph the ordered pairs (and label them) on the coordinate plane.
     If the 3 points you found do not lie in a straight line, find another.
4. Once you have plotted 3 co-linear points, draw the line through the
     points (and label it with its equation.)

Intercepts method:
1. Write the equation in Ax + By = C form.
2. Find the y intercept:
            a. Let x = 0 (substitute 0 for x in the equation)
            b. Calculate the value for y.
            c. The y intercept is in the form:
               (0, the y value you calculated)
3. Find the x intercept:
            a. Let y = 0 (substitute 0 for y in the equation)
            b. Calculate the value for x.
            c. The x intercept is in the form: (x , 0)
4. Graph (and label) the two intercepts on the coordinate plane.
5. Draw the line through the points (and label it with its equation).
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Point slope method:
1. Solve the equation for y (write in y=mx+b form) to find the slope and y-intercept (0,b).
2. Graph the y-intercept on the coordinate plane.
3. Starting at the y-intercept, use the slope to direct you to another point on the line (label the points).
4. Draw the line through the points (and label it with its equation)
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To Graph a Constant Equation
A constant equation will have only one variable, either the x or the y.
1. If the equation is x = c, draw a vertical line through the point
(c ,0). The line will be parallel to the y-axis
and will cross the x-axis at c. (If the y is missing from the equation, the line will never touch the y-axis!)
2. If the equation is y = c, draw a horizontal line through the point (0,c). The line will be parallel to the x-axis
and will cross the y-axis at c. (If the x is missing from the equation, the line will never touch the x-axis!)
3. Label the line with the given equation and the points with their ordered pairs.
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To Graph a Linear Inequality
1. Determine whether the line will be solid or dotted
     if the symbol is < or > the line will be dotted
     if the symbol is < or > the line will be solid
2. Graph the line using one of the methods for graphing equations.
     Remember to graph the correct type of line (dotted or solid)
3. Choose a test point      (any point that does not lie on the line...
     the origin is usually the easiest).
4. Substitute the coordinates of the test point into the original inequality.
If the test point makes the inequality true, it is a solution, so shade the side where the test point is. If the test point makes the inequality false, it is NOT a solution, so shade the OTHER side of the line, NOT the side with the test point.
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