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Systems of Inequalities

Last updated over 2 years ago
25 questions
1

Type the equation of the line in the graph below. y=mx+b

1

Type in a point (x,y) that lies on this line.

1

Does(1,3) lie on this line?

1
  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
Recall that a solution to an equation is a (x,y) point that lies on the line of the equation and therefore makes the equation true.
For Example:

1

Is (1,3) a solution to the equation y=x+2?

1

Type y<x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

4

Select EVERYTHING that's true about the graph of the inequality (#6) y<x+2.

1

Is (1,3) a solution to the inequality? y<x+2?

Notice in the example below, when = changes to < the point on the line is no longer a solution.


1

Type y\le x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

4

Select EVERYTHING that's true about the graph of the inequality (#9) y\le x+2.

1

Is (1,3) a solution to the inequality? y\le x+2?

Notice in the example below, when = changes to \leq the point on the line is still a solution!

1

Type y> x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

4

Select EVERYTHING that's true about the graph of the inequality (#12) y>x+2.

1

Is (1,3) a solution to the inequality? y> x+2?

1

Type y\geq x+2 in the textbox below to see its graph.
Then sketch an accurate graph on your notes sheet & answer the questions below it.

4

Select EVERYTHING that's true about the graph of the inequality (#15) y\geq x+2.

1

Is (1,3) a solution to the inequality? y\geq x+2?

Let's make some conclusions...

1

If the symbols in an inequality are < or > will the line on the graph be solid or dotted?

1

If the symbols in an inequality are \leq or \geq will the line on the graph be solid or dotted?

1

If the symbols in an inequality are < or \leq will the graph be shaded above or below the line?

1

If the symbols in an inequality are > or \geq will the graph be shaded above or below the line?

1

What does the shaded region on a graph represent?

4

Match each graph with its inequality.

  • y<-x+1
  • y\leq -x+1
  • y>-x+1
  • y\geq -x+1

Use this chart to fill in the bottom left graphs on your notes sheet.

1

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
*Clearly show if your line is dotted or solid!
*Clearly show shading above or below the line!

1

Click 'Show Your Work' and graph the inequality. Then select the point that is a solution to the inequality.
*Clearly show if your line is dotted or solid!
*Clearly show shading above or below the line!

Now it's time for the main event...graphing SYSTEMS of inequalities!!!

Check out the process below. I also do two examples in the 5 minute video below. When you're ready to try some, turn your notes sheet over and start graphing!
Still unsure? Watch this 5 minute video.
Ask me to check your graphs in #24 and #25 (or compare them with a partner) before you submit!