4.7 Graphs of linear inequalities  (Page 7/10)

$x=5$

$y=\mathrm{-3}$

$2x+y=5$

$x-y=2$

$y=x+2$

$y=\frac{3}{4}x-1$

Katherine is a private chef. The equation $C=6.5m+42$ models the relation between her weekly cost, C , in dollars and the number of meals, m , that she serves.

1. ⓐ Find Katherine’s cost for a week when she serves no meals.
2. ⓑ Find the cost for a week when she serves 14 meals.
3. ⓒ Interpret the slope and C -intercept of the equation.
4. ⓓ Graph the equation.

Marjorie teaches piano. The equation $P=35h-250$ models the relation between her weekly profit, P , in dollars and the number of student lessons, s , that she teaches.

1. ⓐ Find Marjorie’s profit for a week when she teaches no student lessons.
2. ⓑ Find the profit for a week when she teaches 20 student lessons.
3. ⓒ Interpret the slope and P –intercept of the equation.
4. ⓓ Graph the equation.

$4x-3y=\mathrm{-1};y=\frac{4}{3}x-3$

$2x-y=8;x-2y=4$

$y=5x-1;10x+2y=0$

$3x-2y=5;2x+3y=6$

slope $\frac{1}{3}$ and $y\text{-intercept}$ $\left(0,\mathrm{-6}\right)$

slope $\mathrm{-5}$ and $y\text{-intercept}$ $\left(0,\mathrm{-3}\right)$

slope $0$ and $y\text{-intercept}$ $\left(0,4\right)$

slope $\mathrm{-2}$ and $y\text{-intercept}$ $\left(0,0\right)$

$m=-\frac{1}{4}$ , point $\left(\mathrm{-8},3\right)$

$m=\frac{3}{5}$ , point $\left(10,6\right)$

Horizontal line containing $\left(\mathrm{-2},7\right)$

$m=\mathrm{-2}$ , point $\left(\mathrm{-1},\mathrm{-3}\right)$

$\left(2,10\right)$ and $\left(\mathrm{-2},\mathrm{-2}\right)$

$\left(7,1\right)$ and $\left(5,0\right)$

$\left(3,8\right)$ and $\left(3,\mathrm{-4}\right)$ .

$\left(5,2\right)$ and $\left(\mathrm{-1},2\right)$

line $y=\mathrm{-3}x+6$ , point $\left(1,\mathrm{-5}\right)$

line $2x+5y=\mathrm{-10}$ , point $\left(10,4\right)$

line $x=4$ , point $\left(\mathrm{-2},\mathrm{-1}\right)$

line $y=\mathrm{-5}$ , point $\left(\mathrm{-4},3\right)$

line $y=-\frac{4}{5}x+2$ , point $\left(8,9\right)$

line $2x-3y=9$ , point $\left(\mathrm{-4},0\right)$

line $y=3$ , point $\left(\mathrm{-1},\mathrm{-3}\right)$

line $x=\mathrm{-5}$ point $\left(2,1\right)$

Determine whether each ordered pair is a solution to the inequality $y<x-3$ :

ⓐ $\left(0,1\right)$
ⓑ $\left(\mathrm{-2},\mathrm{-4}\right)$
ⓒ $\left(5,2\right)$
ⓓ $\left(3,\mathrm{-1}\right)$
ⓔ $\left(\mathrm{-1},\mathrm{-5}\right)$

Determine whether each ordered pair is a solution to the inequality $x+y>4$ :

ⓐ $\left(6,1\right)$
ⓑ $\left(\mathrm{-3},6\right)$
ⓒ $\left(3,2\right)$
ⓓ $\left(\mathrm{-5},10\right)$
ⓔ $\left(0,0\right)$

Write the inequality shown by the graph with the boundary line $y=\text{−}x+2$ .

Write the inequality shown by the graph with the boundary line $y=\frac{2}{3}x-3$ .

Write the inequality shown by the shaded region in the graph with the boundary line $x+y=\mathrm{-4}$ .

Write the inequality shown by the shaded region in the graph with the boundary line $x-2y=6.$

Graph the linear inequality $y>\frac{2}{5}x-4$ .

Graph the linear inequality $y\le -\frac{1}{4}x+3$ .

Graph the linear inequality $x-y\le 5$ .

Graph the linear inequality $3x+2y>10$ .

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

Graph the linear inequality $y<6$ .

Plot each point in a rectangular coordinate system.

ⓐ $\left(2,5\right)$
ⓑ $\left(\mathrm{-1},\mathrm{-3}\right)$
ⓒ $\left(0,2\right)$
ⓓ $\left(\mathrm{-4},\frac{3}{2}\right)$
ⓔ $\left(5,0\right)$

Which of the given ordered pairs are solutions to the equation $3x-y=6$ ?

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

Find three solutions to the linear equation $y=\mathrm{-2}x-4$ .

Find the x - and y -intercepts of the equation $4x-3y=12$ .

Find the slope of the line between the points $\left(5,2\right)$ and $\left(\mathrm{-1},\mathrm{-4}\right)$ .

Graph the line with slope $\frac{1}{2}$ containing the point $\left(\mathrm{-3},\mathrm{-4}\right)$ .

$y=\frac{5}{3}x-1$

$y=\text{−}x$

$x-y=2$

$4x+2y=\mathrm{-8}$

$y=2$

$x=\mathrm{-3}$

slope $-\frac{3}{4}$ and y -intercept $\left(0,\mathrm{-2}\right)$

$m=2$ , point $\left(\mathrm{-3},\mathrm{-1}\right)$

containing $\left(10,1\right)$ and $\left(6,\mathrm{-1}\right)$

parallel to the line $y=-\frac{2}{3}x-1$ , containing the point $\left(\mathrm{-3},8\right)$

perpendicular to the line $y=\frac{5}{4}x+2$ , containing the point $\left(\mathrm{-10},3\right)$

Write the inequality shown by the graph with the boundary line $y=\text{−}x-3$ .

$y>\frac{3}{2}x+5$

$x-y\ge \mathrm{-4}$

$y\le \mathrm{-5}x$

$y<3$