Answer:
Graph C represents
x - y < 3 correctly
Step-by-step explanation:
Let us revise some important notes about the solutions of an inequality
- If y ≥ mx + b, then the line is solid and the shaded is above the line
- If y ≤ mx + b, then the line is solid and the shaded is below the line
- If y > mx + b, then the line is dashed and the shaded is above the line
- If y < mx + b, then the line is dashed and the shaded is below the line
∵ The inequality is
x - y < 3
- Put the inequality in the form y less than or greater than m x + b
∵
x - y < 3
- Add y to both sides
∴
x < 3 + y
- Subtract 3 from both sides
∴
x - 3 < y
- That means y is greater than
x - 3
∴ y >
x - 3
∵ The sign of the inequality is >
∴ The line is dashed
∴ The shading is above the line
- Look to the answer to find the correct answer
∵ In figure C, the line is dashed
∵ The shading is above the line
- C only has the two conditions
∴ Graph C represents
x - y < 3 correctly