Lesson video

Hi, I'm Miss Davies.

In this lesson, we're going to representing inequalities on a coordinate grid.

We are going to plot the graph of y is equal to 2x subtract 3.

To do this, we can use a table of values.

We can also look at the equation.

We know that the y intercept is -3 and the gradient is 2.

For every one unit to the right, the graph will go two units up.

We are now going to shade the region in which y is less than or equal to 2x subtract 3.

If we look at the coordinate 3,1 and substitute this into the inequality, this tells us that 1 is less than or equal to 3, which it is.

If we look at the coordinate 1,4 and substitute that into our inequality, it says that 4 is less than or equal to -1, which it isn't.

This means we're going to shade the inequality on this side of the graph.

Have a think about this question.

Pause the video to complete your task and resume once you're finished.

We wouldn't choose a point on the line as this wouldn't tell us which side to shade in.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here's the answer.

y is greater than or equal to 2x add 1.

This means that above the solid line should be shaded.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

y is less than -x add 3.

This means that below at the dash line should be shaded.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

y is greater than or equal to -2x add 4, meaning above the solid line should be shaded in.

If we're going to shade the region where 2y is less than or equal to 3x subtract 2, we need to first make y the subject.

To do this, we divide every term in the inequality by 2.

This gives us y is less than or equal to 3/2 x subtract 1.

We can then draw this line onto our coordinate grid.

Next, we can shade in the region that fits the inequality.

To figure out which side of the line to shade, you can use the coordinate task that we did before.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

This inequality is y is greater than -2x add 6 and above the dash line is shaded.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

This inequality is y is less than or equal to -x add 2, because below the solid line is shaded.

Here is a question for you to try.

Pause the video to complete your task and resume once you're finished.

Here is the answer.

This can be written as y is less than 4/3 x add 8/3, because below the dash line is shaded in.

That's all for this lesson.

Thanks for watching.