2.15.1 Drawing a Graph

To draw the graph of an inequality

• First, rewrite the inequality in slope-intercept form \((y = mx + b)\), 
• Next, plot the y-intercept, (0, b), on the y-axis. This is the point where the graph intersects the y-axis.
• Use the slope to find a second point on the line.
• Draw a straight line through the two points to represent the boundary of the inequality.
  • If the inequality includes the equal sign, draw a solid line; otherwise, draw a dashed line.
  • Shade the region that satisfies the inequality.
  • If the inequality is a system of two or more inequalities, repeat above steps for each inequality and shade the region that satisfies all of the inequalities. The solution is the region where all the shaded regions overlap.

Worked example:

By shading the unwanted regions of the grid, draw and label the region R which satisfies the following three inequalities .

\(y≤2\)               \(x<3\)         \(yx+4\)

Draw the solid line for y=2 and shade the region above the line

Draw the dashed line for \(x=3\) and shade the region right to the line

Draw the solid line for \(y=x+4\) and shade the region above the line.

The remaining unshaded region, R, is the region that fulfills all three inequalities.