You are graphing the inequality $y \leq 5x - 3$. Which statement correctly describes the boundary line?

The line is dashed because the inequality is 'less than or equal to'.

The line is solid because the inequality includes 'or equal to'.

The line is dashed because the slope is positive.

The line is solid because the y-intercept is negative.

5-5 Graphing Inequalities in Two Variables Practice — Grade 9 math

5-5 Graphing Inequalities in Two Variables — Practice Questions

1. When graphing a linear inequality, which of these symbols requires you to draw a solid boundary line?
- A. $<$
- B. $>$
- C. $\geq$
- D. =
2. To correctly graph the linear inequality $y > -x + 9$, you must draw a ___ boundary line.
3. Which of the following ordered pairs is a solution to the system of inequalities $y < x + 1$ and $x + 2y > 6$?
- A. (1, 1)
- B. (4, 2)
- C. (3, 1)
- D. (2, 2)
4. Is the point $(2, 5)$ a solution to the system of inequalities $y \geq 3x - 1$ and $y < x + 2$? Answer Yes or No. ___
5. You are graphing the inequality $y \leq 5x - 3$. Which statement correctly describes the boundary line?
- A. The line is dashed because the inequality is 'less than or equal to'.
- B. The line is solid because the inequality includes 'or equal to'.
- C. The line is dashed because the slope is positive.
- D. The line is solid because the y-intercept is negative.
6. Which point is a solution to the inequality $y < \frac{1}{2}x$?
- A. $(6, 3)$
- B. $(2, 2)$
- C. $(-4, -1)$
- D. $(8, 3)$
7. Which point is a solution to the inequality $x + 3y \leq 0$?
- A. $(1, 1)$
- B. $(3, -1)$
- C. $(-2, 1)$
- D. $(0, 1)$
8. When graphing the inequality $3x - 2y < 6$, you test the point $(4, 1)$. The substitution results in the statement $10 < 6$, which is false. Which region should be shaded?
- A. The half-plane containing $(4, 1)$
- B. The half-plane not containing $(4, 1)$
- C. The boundary line only
- D. The entire coordinate plane
9. To test if the point $(-1, 5)$ is in the solution set of $2x + y > 3$, you must first evaluate the expression $2x + y$. What is the value of this expression at the given point? ___
10. If testing the point $(0, 0)$ in the inequality $y > mx + b$ results in a true statement, what must be true about the graph's shaded region?
- A. It is the region below the boundary line.
- B. It is the region containing the origin.
- C. The boundary line passes through the origin.
- D. It is the region not containing the origin.