Algebra I: Solving and Graphing Linear Inequalities on a Number Line

The graph is the boundary line for the inequality y≤ 1/3x + 3. Which of the points is a solution for this inequality?

• (1,4)

• (-6,2)

• (0,4)

• (2,3)

Solve the system of inequalities by graphing.

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Colin needs to save at least $200 for the upcoming Valentine's Dance. He works 2 jobs earning $9/hour babysitting and $25/hour mowing lawns. He only has time to work 16 hours before the dance. Which system of inequalities models correctly the hours that Colin can work before the dance.

• x + y ≥ 25

  x + y ≤ 9

• 100x + 25 y ≤ 200

  2x + 9y ≤ 16

• x + y ≥ 200

  9x + 25y ≤ 16

• 9x + 25y ≥ 200

  x + y ≤ 16

A catering company charges $250 plus $50 per guest for a wedding. Justin and Logan do not want to spend than $7,000 on catering. Write and solve an inequality in terms of the number of guests, g, that can be invited.

• (3, -2)

• (-6, 0)

• (5, 6)

• (-2, 4)

Lennox plans to earn at least $240 babysitting and mowing lawsn this summer. She will charge $4 per hour babysitting and $3 per hour mosing lawns. She would like to work a maximum of 50 hours this summer. She wrote the following system of linear inequalities to determine combinations of jobs she can do. Let x = the number of hours spent babysitting, and y = the number of hours spent mowing lawns. 12x + 11y ≥ 300 x+y≤50 Select the choice that will earn her at least $240, but will not require more than 50 hours per week.

• 20 hours of babysitting and 50 hours of mowing lawns

• 30 hours of babysitting and 40 hours of mowing lawns

• 20 hours of babysitting and 20 hours of mowing lawns

• 10 hours of babysitting and 10 hours of mowing lawns

• 30 hours of babysitting and 10 hours of mowing lawns

Rate of change also means______

• x-intercept

• y-intercept

• slope

• my "b" value 

When graphing linear inequalities, I know that a ≤ or ≥ means I will draw a....

• solid line

• dotted line

Solve the following:
-2y≥ 2x + 4

• y≥-1x - 2

• y≤-1x - 2

• y≥ 1x + 2

• y≤1x + 2

In the inequality y > 2x + 4, I would shade __________ the line.

• above

• below