Describe and use regions on a graph when some boundaries are strict and some are not: dashed and solid lines, which side to shade, whole-number points in a region, the greatest value of an expression there, and boundaries you have to find yourself.
What you will learn
- Draw a strict inequality as a dashed line and an inclusive one as a solid line
- Find the right side of a line by testing a point
- Count whole-number points in a region, leaving out points on dashed lines
- Find the greatest value of an expression such as 2x + y over the whole-number points in a region
- Find the equation of a boundary from two points on it, then write its inequality
Dashed or solid
Every inequality in two variables has a boundary line.
Draw it dashed for < or > (the points on the line are not included) and solid for ≤ or ≥ (they are). Reading a graph works the other way: a dashed edge means a strict inequality.
Read the question for the shading: usually the region R is shaded, but some questions ask you to leave R unshaded and shade the parts you do not want.
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- Dashed or solid
- Which side? Test a point
- Whole-number points
- A boundary you have to find
8 practice questions, marked as you go; about 30 minutes in all.
Key terms
Solid
In this unit: Graphs and coordinates: shapes on axes, regions, areas and tangents
More graphs and coordinate geometry: shapes on coordinate axes, gradients and perpendicular lines in shapes, regions with strict and inclusive boundaries, the area under a curve from trapezia, and the gradient at a point from a tangent.
- Shapes on coordinate axes
- Gradients and lines in shapes
- Regions in depth
- Area under a curve
- Gradient at a point, and the kinematics formulae
All of Graphs and coordinates: shapes on axes, regions, areas and tangents