Why is the boundary line for $7x + y \geq 1$ graphed as a solid line?

Because the points on the line are included in the solution.

Because the points on the line are not included in the solution.

Because the slope of the line is negative.

Because the y-intercept is positive.

Linear Inequalities in Two Variables Practice — Grade 11 math

Lesson 4: Linear Inequalities in Two Variables — Practice Questions

1. What is the equation of the boundary line for the linear inequality $5x - 2y < 10$? The equation should be in the form $Ax + By = C$.
2. When graphing the linear inequality $y \geq -3x + 4$, what type of line should be used for the boundary?
- A. Solid
- B. Dashed
- C. Dotted
- D. Curved
3. Which of the following inequalities would have its boundary line graphed as a dashed line?
- A. $y > 8x - 5$
- B. $y \leq 8x - 5$
- C. $y \geq 8x - 5$
- D. $2x = 8y$
4. The boundary line for an inequality is the horizontal line $y = -4$. If this line is graphed as solid, a possible inequality is $y \leq$ ___.
5. Why is the boundary line for $7x + y \geq 1$ graphed as a solid line?
- A. Because the points on the line are included in the solution.
- B. Because the points on the line are not included in the solution.
- C. Because the slope of the line is negative.
- D. Because the y-intercept is positive.
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.