Lesson video

Hi, I'm Miss Davies.

In this lesson we're going to be identifying the inequalities from a shaded region.

In this example, we are going to state the inequalities that the shaded region satisfies.

If we look at this first line, we can see that it goes through the point x = 1.

As it is a solid line, and the shaded region is to the right of the line, the inequality is x is greater than or equal to 1.

With our next line, this cuts through the point where y = -1.

As it is a dashed line and all the shaded region is above it, the inequality is y is greater than -1.

With our third line, the y intersect is 4, and it has a gradient of -1.

This means that the equation is y = -x, add 4.

Because this is a dashed line and the shaded region is below it, we can say that y is less than -x, add 4.

These are the three inequalities that the shaded region satisfies.

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 shaded region represents x is greater than 0, y is greater than or equal to -1, and y is less than or equal to 1/2 x, add one.

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 shaded region represents y is greater than or equal to -2x, subtract 1, y is less than 1/2 x, add 1/2, and y is greater than x, subtract one.

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 shaded region is represented by y is less than -4x, add 4.

y is greater than 6x, subtract 2, and y is greater than or equal to 4/3 x, subtract 4.

Here's a question for you to try.

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

Here is the answer.

This shaded region is represented by the inequalities y is less than or equal to 4, y is greater than or equal to 4/3 x, subtract 4, y is less than 8x, subtract 4, and y is less than -4x, add 12.

That's all for this lesson.

Thanks for watching.