Solve the inequality for y by converting the equation to slope intercept form (Y = mx + b), where
m is the slope of the line and b is the y-intercept. Here is an example:
y + 5 ≤ 2x + 2
y ≤ 2x - 3
Plot the y-intercept (-3) on the y axis. That is your first point on the graph.
Plot a few other points off the y-intercept by using the slope of the line, which is 2 in this example. Convert the slope into a rise/run fractional form. Rise will be the vertical distance from the y-intercept, while run is the horizontal. In our example of y ≤ 2x - 3, the rise/run fractional form of the slope is 2/1.
You can also plot as opposites, if needed ( -2/-1 ).
Connect the points in a straight line, which creates a boundary line. Determine whether the line is solid or dashed. A solid line includes the points on the lines as solutions, while a dashed line does not include those points.
If the inequality is expressed as y≥ or y≤, the points on the boundary line are solutions, and the line is solid.
If the inequality is expressed as y> or y<, the points on the boundary line are not solutions, and the line is dashed.
Shade the graph either below or above the boundary line, depending on the direction of the inequality sign. If the inequality is expressed as y> or y≥, the points above the boundary line are solutions and should be shaded. If the inequality is expressed as y< or y≤, the points below the boundary line are solutions and should be shaded.
Follow the same process with any other equations in the system. Color coding is helpful in isolating the solutions for each equation.
The overlapped regions of the graph represent the solution of the system and include all the ordered pairs that meet the requirement for all of the inequalities in the system. Solutions can be verified by
substituting the numbers into the original equations.