4.7 Graphs of linear inequalities  (Page 5/10)

Graph the linear inequality $y>4x$ .

Graph the linear inequality $y>x$ .

Graph the linear inequality $y\le \text{−}x$ .

Graph the linear inequality $y\le \mathrm{-3}x$ .

Graph the linear inequality $y\ge \mathrm{-2}$ .

Graph the linear inequality $y<\mathrm{-1}$ .

Graph the linear inequality $y<4$ .

Graph the linear inequality $y\ge 2$ .

Graph the linear inequality $x\le 5$ .

Graph the linear inequality $x>\mathrm{-2}$ .

Graph the linear inequality $x>\mathrm{-3}$ .

Graph the linear inequality $x\le 4$ .

Graph the linear inequality $x-y<4$ .

Graph the linear inequality $x-y<\mathrm{-3}$ .

Graph the linear inequality $y\ge \frac{3}{2}x$ .

Graph the linear inequality $y\le \frac{5}{4}x$ .

Graph the linear inequality $y>\mathrm{-2}x+1$ .

Graph the linear inequality $y<\mathrm{-3}x-4$ .

Graph the linear inequality $x\le \mathrm{-1}$ .

Graph the linear inequality $x\ge 0$ .

Money. Gerry wants to have a maximum of $100 cash at the ticket booth when his church carnival opens. He will have $1 bills and $5 bills. If x is the number of $1 bills and y is the number of $5 bills, the inequality $x+5y\le 100$ models the situation.

1. ⓐ Graph the inequality.
2. ⓑ List three solutions to the inequality $x+5y\le 100$ where both x and y are integers.

Shopping. Tula has $20 to spend at the used book sale. Hardcover books cost $2 each and paperback books cost $0.50 each. If x is the number of hardcover books Tula can buy and y is the number of paperback books she can buy, the inequality $2x+\frac{1}{2}y\le 20$ models the situation.

1. ⓐ Graph the inequality.
2. ⓑ List three solutions to the inequality $2x+\frac{1}{2}y\le 20$ where both x and y are whole numbers.

Lester thinks that the solution of any inequality with a>sign is the region above the line and the solution of any inequality with a<sign is the region below the line. Is Lester correct? Explain why or why not.

Explain why in some graphs of linear inequalities the boundary line is solid but in other graphs it is dashed.

ⓐ $\left(\mathrm{-1},\mathrm{-5}\right)$
ⓑ $\left(\mathrm{-3},4\right)$
ⓒ $\left(2,\mathrm{-3}\right)$
ⓓ $\left(1,\frac{5}{2}\right)$

ⓐ $\left(4,3\right)$
ⓑ $\left(\mathrm{-4},3\right)$
ⓒ $\left(\mathrm{-4},\mathrm{-3}\right)$
ⓓ $\left(4,\mathrm{-3}\right)$

ⓐ $\left(\mathrm{-2},0\right)$
ⓑ $\left(0,\mathrm{-4}\right)$
ⓒ $\left(0,5\right)$
ⓓ $\left(3,0\right)$

ⓐ $\left(2,\frac{3}{2}\right)$
ⓑ $\left(3,\frac{4}{3}\right)$
ⓒ $\left(\frac{1}{3},\mathrm{-4}\right)$
ⓓ $\left(\frac{1}{2},\mathrm{-5}\right)$

$5x+y=10$

ⓐ $\left(5,1\right)$
ⓑ $\left(2,0\right)$
ⓒ $\left(4,\mathrm{-10}\right)$

$y=6x-2$

ⓐ $\left(1,4\right)$
ⓑ $\left(\frac{1}{3},0\right)$
ⓒ $\left(6,\mathrm{-2}\right)$

$y=4x-1$

$y=-\frac{1}{2}x+3$

$x+2y=5$

$3x+2y=6$

$x+y=3$