Graphing Linear One-Step Inequalities

Multi-Step Equations with Variables on Both Sides - How it Works - Video

Example 1 Part 1

Example 1 Part 1:

We have the inequality, y - 2x ≤ 4, which we need to graph.

When graphing linear inequalities, our first step is graph the line. There are more multiple ways of doing that including leaving it standard form and finding the intercepts, putting in slope intercept form, or something else. Here we left our inequality in standard form and found our x-intercept and y-intercept.

We can solve the inequality just like we do with equations.

Example 1 Part 2

Example 1 Part 2:

Next we need to start graphing. There are multiple ways of doing including using the slope and the intercept or making tables. Here we substitute two input values and plot the points.

Now that we have our two points for the line we can draw a solid line for the inequality since we have less than or equal to.

Example 1 Part 3

Example 1 Part 3:

Now, we need to pick two points, one on either side of the solid line. Here we have picked (0, 0) and (4, 0). Next we need to plug those points into the either the given inequality or the one you solved for. We are going to use the given.

Now we know the blue point, (4, 0), is true. We can shade the entire section that contains the blue point. And that is our answer.

Example 2 Part 1

Example 2 Part 1:

We have the inequality, -2y < 3x -2, which we need to graph.

When graphing linear inequalities, our first step is graph the line. There are more multiple ways of doing that including leaving it standard form and finding the intercepts, putting in slope intercept form, or something else. Here we left our inequality in standard form and found our x-intercept and y-intercept.

We can solve the inequality just like we do with equations.

Now, we plot the two points and draw our solid line. Since our two points are on the line, when we plot them, they are closed circles because we have greater than or equal to.

Example 2 Part 2

Example 2 Part 2:

Next we need to start graphing. There are multiple ways of doing including using the slope and the intercept or making tables. Here we use that method instead of substituting two inputs.

We found the y-intercept, which is 1, which is on the y-axis. After that, we used the slope to find the next. The first point is up 3 and to the left 2 and the second point is down 3 and to the right 2.

Now we can add dotted line since we have less than.

Example 2 Part 3

Example 2 Part 3:

Now, we need to pick two points, one on either side of the solid line. Here we have picked (-3, 1) and (4, 2). Next we need to plug those points into the either the given inequality or the one you solved for. We are going to use the given.

Now we know the blue point, (4, 2), is true. We can shade the entire section that contains the blue point. And that is our answer.

Live Worksheet

Teacher - Edpuzzle Link