# 4.7 Graphs of linear inequalities  (Page 4/10)

 Page 4 / 10

Graph the linear inequality $y<5$ .

Graph the linear inequality $y\le -1$ .

## Key concepts

• To Graph a Linear Inequality
1. Identify and graph the boundary line.
If the inequality is $\le \text{or}\ge$ , the boundary line is solid.
If the inequality is<or>, the boundary line is dashed.
2. Test a point that is not on the boundary line. Is it a solution of the inequality?
3. Shade in one side of the boundary line.
If the test point is a solution, shade in the side that includes the point.
If the test point is not a solution, shade in the opposite side.

## Practice makes perfect

Verify Solutions to an Inequality in Two Variables

In the following exercises, determine whether each ordered pair is a solution to the given inequality.

Determine whether each ordered pair is a solution to the inequality $y>x-1$ :

$\left(0,1\right)$
$\left(-4,-1\right)$
$\left(4,2\right)$
$\left(3,0\right)$
$\left(-2,-3\right)$

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

$\left(0,0\right)$
$\left(2,1\right)$
$\left(-1,-5\right)$
$\left(-6,-3\right)$
$\left(1,0\right)$

yes  no  no  yes  no

Determine whether each ordered pair is a solution to the inequality $y :

$\left(0,3\right)$
$\left(-3,-2\right)$
$\left(-2,0\right)$
$\left(0,0\right)$
$\left(-1,4\right)$

Determine whether each ordered pair is a solution to the inequality $y :

$\left(-3,0\right)$
$\left(1,6\right)$
$\left(-6,-2\right)$
$\left(0,1\right)$
$\left(5,-4\right)$

yes  no  no  yes  yes

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

$\left(5,1\right)$
$\left(-2,6\right)$
$\left(3,2\right)$
$\left(10,-5\right)$
$\left(0,0\right)$

Determine whether each ordered pair is a solution to the inequality $x+y>2$ :

$\left(1,1\right)$
$\left(4,-3\right)$
$\left(0,0\right)$
$\left(-8,12\right)$
$\left(3,0\right)$

no  no  no  yes  yes

Recognize the Relation Between the Solutions of an Inequality and its Graph

In the following exercises, write the inequality shown by the shaded region.

Write the inequality shown by the graph with the boundary line $y=3x-4.$

Write the inequality shown by the graph with the boundary line $y=2x-4.$

$y<2x-4$

Write the inequality shown by the graph with the boundary line $y=-\frac{1}{2}x+1.$

Write the inequality shown by the graph with the boundary line $y=-\frac{1}{3}x-2.$

$y\le -\frac{1}{3}x-2$

Write the inequality shown by the shaded region in the graph with the boundary line $x+y=5.$

Write the inequality shown by the shaded region in the graph with the boundary line $x+y=3.$

$x+y\ge 3$

Write the inequality shown by the shaded region in the graph with the boundary line $2x+y=-4.$

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

$x+2y\ge -2$

Write the inequality shown by the shaded region in the graph with the boundary line $3x-y=6.$

Write the inequality shown by the shaded region in the graph with the boundary line $2x-y=4.$

$2x-y<4$

Write the inequality shown by the shaded region in the graph with the boundary line $2x-5y=10.$

Write the inequality shown by the shaded region in the graph with the boundary line $4x-3y=12.$

$4x-3y>12$

Graph Linear Inequalities

In the following exercises, graph each linear inequality.

Graph the linear inequality $y>\frac{2}{3}x-1$ .

Graph the linear inequality $y<\frac{3}{5}x+2$ .

Graph the linear inequality $y\le -\frac{1}{2}x+4$ .

Graph the linear inequality $y\ge -\frac{1}{3}x-2$ .

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

Graph the linear inequality $x-y\ge -2$ .

Graph the linear inequality $4x+y>-4$ .

Graph the linear inequality $x+5y<-5$ .

Graph the linear inequality $3x+2y\ge -6$ .

Graph the linear inequality $4x+2y\ge -8$ .

Two sisters like to compete on their bike rides. Tamara can go 4 mph faster than her sister, Samantha. If it takes Samantha 1 hour longer than Tamara to go 80 miles, how fast can Samantha ride her bike?
8mph
michele
16mph
Robert
3.8 mph
Ped
16 goes into 80 5times while 20 goes into 80 4times and is 4mph faster
Robert
what is the answer for this 3×9+28÷4-8
315
lashonna
how do you do xsquard+7x+10=0
What
(x + 2)(x + 5), then set each factor to zero and solve for x. so, x = -2 and x = -5.
bruce
I skipped it
What
In 10 years, the population of Detroit fell from 950,000 to about 712,500. Find the percent decrease.
how do i set this up
Jenise
25%
Melissa
25 percent
Muzamil
950,000 - 712,500 = 237,500. 237,500 / 950,000 = .25 = 25%
Melissa
I've tried several times it won't let me post the breakdown of how you get 25%.
Melissa
Subtract one from the other to get the difference. Then take that difference and divided by 950000 and you will get .25 aka 25%
Melissa
Finally 👍
Melissa
one way is to set as ratio: 100%/950000 = x% / 712500, which yields that 712500 is 75% of the initial 950000. therefore, the decrease is 25%.
bruce
twenty five percent...
Jeorge
thanks melissa
Jeorge
950000-713500 *100 and then divide by 950000 = 25
Muzamil
Jeannette has $5 and$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
6t+3
Melissa
6t +3
Bollywood
Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original salary? Iris Reply let us suppose her original salary is 'm'. so, according to the given condition, m*(6/100)=30 m= (30*100)/6 m= 500 hence, her original salary is$500.
Simply
28.50
Toi
thanks
Jeorge
How many pounds of nuts selling for $6 per pound and raisins selling for$3 per pound should Kurt combine to obtain 120 pounds of trail mix that cost him $5 per pound? Valeria Reply Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost$8 per square foot and decorator tiles that code $20 per square foot. How many square feet of each tile should she use so that the overal cost of he backsplash will be$10 per square foot?
I need help with maths can someone help me plz.. is there a wats app group?
WY need
Fernando
How did you get $750? Laura Reply if y= 2x+sinx what is dy÷dx formon25 Reply does it teach you how to do algebra if you don't know how Kate Reply Liam borrowed a total of$35,000 to pay for college. He pays his parents 3% interest on the $8,000 he borrowed from them and pays the bank 6.8% on the rest. What average interest rate does he pay on the total$35,000? (Round your answer to the nearest tenth of a percent.)
exact definition of length by bilbao
the definition of length
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francemichael
exact meaning of length
francemichael
exact meaning of length
francemichael
how many typos can we find...?
5
Joseph