3.03 Graphs of inequalities in two variables
State whether the given coordinates are solutions to the inequalities:
\left(6, 20\right)\,; \enspace y \geq 4 x + 5
\left(3, 2\right)\,; \enspace 3 x + 2 y\geq12
State whether each of the given points satisfies the following inequalities:
\left(-1, - 7 \right)
\left(12, 16\right)
\left(13, 6\right)
\left(8, - 5 \right)
\left(9, 15\right)
\left( - 1 , - 2 \right)
\left(0, 0\right)
\left(1, 4\right)
\left(5, - 52 \right)
\left( - 1 , 3\right)
\left( - 3 , 26\right)
\left(1, - 11 \right)
Write the inequality that describes the shaded region in the following graphs:
Consider the equation 2 x + 5 y = 10:
State the x-coordinate of the x-intercept.
State the y-coordinate of the y-intercept.
Graph the line on a coordinate plane.
Write the inequality that describes the region on the graph where \left(- 20,11\right) is located.
Consider the line 4 x + 3 y = 12:
State the x-coordinate of the x-intercept.
State the y-coordinate of the y-intercept.
Graph the solutions to 4 x + 3 y \gt 12.
Do the points on the line satisfy the inequality 4 x + 3 y \gt 12?
Consider the line y = - 2 x + 2:
State the x-coordinate of the x-intercept.
State the y-coordinate of the y-intercept.
State whether the following points satisfies the inequality y \leq- 2 x + 2:
\left(2, 3\right)
\left(3, - 6 \right)
\left(4, - 2 \right)
\left(1, 2\right)
Graph the solutions to y \leq - 2 x + 2.
Do the points on the line satisfy the inequality y \leq- 2 x + 2?
Consider the line y = - 3 x - 6:
State the x-coordinate of the x-intercept.
State the y-coordinate of the y-intercept.
State whether each of the following points satisfies the inequality y \lt- 3 x - 6:
\left( - 7 , 2\right)
\left( - 6 , 3\right)
\left(3, - 2 \right)
\left( - 6 , - 3 \right)
Graph the solutions to y \lt - 3 x - 6.
Consider the graph of y = x - 2:
Graph the solutions to y \gt x - 2.
Graph the solutions to y\leq x - 2.
Consider the inequality y\geq x+ 5:
Graph y = x + 5.
State whether the following points satisfies y\geq x + 5:
\left(3, 10\right)
\left( - 3 , - 2 \right)
Graph the solutions to y\geq x + 5.
Consider the inequality y \gt 2 x - 4:
Graph y = 2 x - 4.
State whether the following points satisfies y \gt 2 x - 4.
\left(1, - 4 \right)
\left(0, - 1 \right)
Graph the solutions to y \gt 2 x - 4.
Consider the inequality 2 x + 3 y \lt 12:
Graph 2 x + 3 y = 12.
State whether each of the following points satisfies 2 x + 3 y \lt12:
\left(2, 4\right)
\left( - 4 , 5\right)
Graph the solutions to 2 x + 3 y \lt12.
Consider the equation 6 x + 3 y = 12:
Complete the following table of values:
| x | 0 | 1 | 2 |
|---|---|---|---|
| y |
State whether each of the following points satisfies the inequality 6 x + 3 y \gt 12:
\left( - 2 , - 2 \right)
\left(3, 1\right)
\left(0, - 1 \right)
\left( - 1 , 2\right)
Graph the solutions to 6 x + 3 y \gt 12.
Graph the following inequalities:
Consider each of the following conditions:
Find the slope of the boundary line.
State the equation of the boundary line in the form y = m x + b.
State the inequality that satisfies the given conditions.
A linear inequality has solutions of \left(0, - 5 \right) and \left( - 1 , - 9 \right) on its boundary line and is not satisfied by \left(1, 3\right).
A linear inequality has solutions of \left(0, - 6 \right) and \left( - 6 , - 24 \right) on its boundary line and is satisfied by \left( - 3 , - 10 \right).
For each of the following inequalities, state whether they are represented using a solid or dashed line on a graph.
State which of the following points lie in each of the given shaded regions:
- \left(2,4\right)
- \left(-3,2\right)
- \left(-1,-6\right)
- \left(3,-3\right)
For each of the following inequalities: