Math 1 · Unit 5 · Lesson 3 · part 2 of 6
Read the region, write the inequality
Given a graphed region, you can write its inequality by reading three clues, in this order.
Read the region, write the inequality
Given a graphed region, you can write its inequality by reading three clues, in this order.
- 1The boundary: m and bRead the line the way Unit 3 taught: b where it crosses the y-axis, m as rise over run. That gives y = mx + b, the equals-sign version.
- 2The line style: strict or inclusiveDashed means a strict sign, < or >. Solid means an inclusive sign, ≤ or ≥.
- 3The shaded side: greater or lessShaded above means y greater than the line. Shaded below means y less than. Put the sign together from clues 2 and 3.
Worked: read this region
The boundary crosses the y-axis at 2 and falls 1 for every 1 right: y = −x + 2. It is dashed: strict. The shading is below: y less than. y < −x + 2.
Optional check: (0, 0) is in the shaded part, and 0 < 2 is true.
Worked: read this one
Boundary crosses at −1, rises 1 for every 2 right: y = 12x − 1. Solid: inclusive. Shaded above: y greater than or equal. y ≥ 12x − 1.
Vertical and horizontal. A vertical boundary at x = a with shading to the right is x > a (or ≥ if solid); to the left is x < a. A horizontal boundary at y = a shaded above is y > a; below is y < a.