Linear Inequalities

Match the appropriate graph to it's linear inequality.

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• (12, -8)

• (4, -4)

• (-4, -10)

• (0, -6)

• (8, -8)

• (6, 3)

• (-6, -3)

• (10, 7)

• (9, -7)

• (-12, -2)

• (12, 1)

• (-12, -7)

• (2,-2)

• (-2,5)

• (1,-2)

• (-3,-5)

Mohal and his children went into a restaurant and will buy drinks and tacos. He must buy no less than 14 drinks and tacos altogether and spend at most $110. Each taco is $4 and each drink is $3. Choose the inequalities that would best represent the scenario for the number of drinks purchased, x, and the number of tacos purchased, y.

• 14x + y ≤ 110

• 4x + 3y ≤ 110

• x + y ≥ 14

• 4x + 3y ≥ 14

Gabriel and his children went into a bakery to buy x donuts and y brownies. Each donut costs $2 and each brownie costs $3. Gabriel wants to spend no more than total of $30 on donuts and brownies. Write an inequality that would represent this scenario.

• 2x + 3y ≥ 30

• 3x + 2y ≥ 30

• 2x + 3y ≤ 30

• 2x + 3y < 30

Jason has some nickels and some dimes. He has no less than 18 coins worth no more than $1.20 combined. If Jason has 4 dimes, determine the maximum number of nickels that he could have.

Penelope and her children went into a grocery store where they sell apples for $0.25 each and peaches for $1 each. Penelope has $20 to spend and must buy a minimum of 12 apples and peaches altogether. If Penelope decided to buy 5 apples, determine the maximum number of peaches that she could buy.

Kaylee is working two summer jobs, making $7 per hour babysitting and making $15 per hour clearing tables. In a given week, she can work no more than 30 total hours and must earn at least $210. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write a system of inequalities. Give each inequality in slope-intercept form.