State whether the following inequalities are represented using a solid line or a dashed line on a graph:
y - 3 x > 5
x \geq 4
- 2 y + x \leq - 10
y + 3 x > 7
- y - 6 x > 0
y + 3 x \leq - 10
y \geq - 2
3 y + 3 x > 4
Write the inequality that describes the following shaded regions:
Is \left(6, 20\right) a solution of y\geq 4 x + 5?
Is \left(3, 2\right) a solution of 3 x + 2 y \geq 12 ?
Determine which point satisfies each of the following inequalities:
Describe the three steps required to graph the inequality y + 7 x \geq 5.
Consider the inequality y \lt- 3 x - 6.
Solve for the x and y-intercepts of the line y = - 3 x - 6.
Determine which of the following points satisfy the inequality y \lt- 3 x - 6:
Hence sketch the graph of y \lt - 3 x - 6.
Do the points on the line satisfy the inequality?
Consider the inequality y \leq - 2 x + 2.
Solve for the x and y intercepts of the line y = - 2 x + 2.
Determine which of the following points satisfies the inequality y \leq - 2 x + 2:
Hence sketch the graph of y \leq - 2 x + 2.
Do the points on the line satisfy the inequality?
The solutions to the equation y = x - 2 are plotted on the following graph:
Graph the solutions to y \gt x - 2.
Graph the solutions to y \leq x - 2.
Sketch the graphs of the following inequalities:
y \gt 2x - 4
y \leq 3 x - 4
y \lt 3x - 9
y \geq - 2x + 4
y \gt 2x - 4
y \leq x + 5
State the linear inequality that satisfies the following:
A linear inequality has solutions of \left(0, - 5 \right) and \left( - 1 , - 9 \right) on its boundary line and is not satisifed 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 satisifed by \left( - 3 , - 10 \right).
Consider the function xy=4.
Sketch the graph of xy=4.
Shade the region where xy \geq 4 for x \geq 0.
Graph the following regions for x\geq 0:
Graph the following regions for x\leq 0: