Graphing Linear Inequalities in the Plane

Consider the set

• Is (0; 0) in S? How can you tell?

• Is (2; 3) in S? How can you tell?

• Is (4; 12) in S? How can you tell?

• Name a point in S with negative x -coordinate._________
• Name a point in S with integer coordinates (other than the one above).___________
• On the grid, plot all 5 points listed above, using • for points in S and × for points
not in S. Make sure to choose a scale for your graph so that all of the points above
fit on the diagram.

Now you will graph S on the same graph that you plotted the points .
• Write the equation for the line that will be the boundary of the set S.

• Put the line in slope -intercept form. (This involves solving for y.)
What is the slope ?___________
What is the y- intercept ?___________

• Find the x- intercept of the line . (This involves substituting y = 0 into the formula
for your line , and solving for x . Do you know why that gets you the x-intercept? )

• Graph the line .
• Shade S.