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9-12 Integrated Math 1 Unit 7 Lesson 4

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Unit 7, Lesson 4

Graphing Linear Inequalities in Two Variables (Part 1)

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Integrated Math 1

Practice

Problem 1

Here is a graph of the equation .

Are the points and solutions to the equation? Explain or show how you know.
Check if each of these points is a solution to the inequality :
Shade the region that represents the solution set to the inequality .
Are the points on the line included in the solution set? Explain how you know.

<p>Graph of a line.</p>

Problem 2

Select all coordinate pairs that are solutions to the inequality .

Problem 3

Consider the linear equation .

The pair is a solution to the equation. Find another pair that is a solution to the equation.
Are and solutions to the inequality ? Explain how you know.
Explain how to use the answers to the previous questions to graph the solution set to the inequality .

Problem 4

The boundary line on the graph represents the equation . Write an inequality that is represented by the graph.

<p><strong>Inequality graphed on a coordinate plane, origin O. Each axis from negative 4 to 4, by 2’s. Dashed line goes through 0 comma 3 and 2 comma negative 2. The region below the dashed line is shaded.</strong></p>

Problem 5

Choose the inequality whose solution set is represented by this graph.

<p>Inequality graphed on a coordinate plane.</p>

Problem 6

ForLesson 14: Solving Systems by Elimination (Part 1)

Solve each system of equations without graphing.

Problem 7

ForLesson 15: Solving Systems by Elimination (Part 2)

Mai and Tyler are selling items to earn money for their elementary school. The school earns dollars for every wreath sold and dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10 wreaths and 7 potted plants and the school earns $62.50.

This situation is represented by this system of equations:

Explain why it makes sense in this situation that the solution of this system is also a solution to .

Problem 8

ForLesson 1: Representing Situations with Inequalities

Elena is planning to go camping for the weekend and has already spent $40 on supplies. She goes to the store and buys more supplies.

Which inequality represents , the total amount in dollars that Elena spends on supplies?

Problem 9

ForLesson 2: Solutions to Inequalities in One Variable

Solve this inequality:

Problem 10

ForLesson 2: Solutions to Inequalities in One Variable

Which graph represents the solution to ?

Problem 11

ForLesson 3: Writing and Solving Inequalities in One Variable

Solve . Explain how to find the solution set.

Problem 12

ForLesson 16: More Symmetry

Identify any angles of rotation that create symmetry.

<p>Flower on polar grid. Grid is made up of 3 circles with the same center. Flower is made up of 3 congruent petals, equally spaced. 2 petals on top half of grid, 1 petals on bottom. Petal length reaches the third outermost circle on the grid.</p>