Name______Date______Teacher______Group______
ALGEBRA
1. Select all of the following equations that represent a nonlinear function.
a. b.
c. d.
2. Fill in the numbers for the table that would make the table represent a linear function.
x / / / 3y / / / 1
3. What are TWO ways in which one could identify the table below as being linear?
x / / / 1 / 3y / / / / 7
______
______
4. Which of the graphs below best represents that of a linear function?
a.b.c. d.
5. Trinity is sketching a graph of the relationship between inches and feet. After she made a table of values she plotted the ordered pairs to create the graph seen below:
Part A. Create a table of values that represents the relationship between feet (x) and inches (y) that represents Trinity’s graph. Then create a table that Trinity should have used.
Trinity’s TableYour Table
Part B. Write the linear equation based on the information from your table above, in which frepresents the number of feet and gh represents the number of inches. Choose two values for x to plug into the equation to determine if the equation correctly reflects your table (show your work).
Equation:______
______
Part C. The graph Trinity created, though incorrect, was still linear. How is that possible? Explain what Trinity did wrong when sketching her graph.
______
6. Which of the following proportional relationships has the same rate of change as the table shown below?
x / 3 / 4 / 6 / 9y / 6 / 8 / 12 / 18
a. b.
c. d.
7. The following equation has infinitely many solutions. Determine the number or term for the space provided.
8. Which of the equations best represents the graph shown below?
9. Is the solution to the equation ? Show your work below to either show the solution is or is not the solution.
______
10. Choose all of the following answer choices that represent a function.
a. b.
c. d.
x / 5 / / 6 /y / 0 / 21 / 2 / 13
11. What is the solution to the system of equations?
a. b.
c. d.
12. A right triangle is made up of two acute angles, and . The measure of is 64 greater than the measure of . What are the measures of and ?
______
13. Choose the TWO systems of linear equations that have exactly ONE solution.
a. b.
c. d.
14. Use the coordinate plane below to solve the system of equations.
15. Which statement is true regarding the two equations shown below?
a. b.
c. d. ghas a solution but h does not
16. The graph below represents a proportional relationship between x and y.
17. Neil is determining the equation given to him in a graph. He notices that the graph is linear and crosses through the points and Neil’s answer of is the value for the slope of the equation he calculated. Which of the following choices is the best answer?
a. Neil’s answer of is the correct answer for the slope of the line.
b. Neil’s answer of is the incorrect answer for the slope of the line. The slope of the line Neil should have calculated is
c. Neil’s answer of is the incorrect answer for the slope of the line. The slope of the line Neil should have calculated is indeterminate since it is a vertical line.
d. Neil’s answer of is the incorrect answer for the slope of the line. The slope of the line Neil should have calculated is 10.
18. Determine which of the following proportional relationships has the greatest rate of change. Let x represent the number of casts and y represent the number of fish caught.
b.
c.d.
19. Circle each answer choice that represents a linear relationship.
a. b.c. d.
e. f. g. h.
20. In Millie’s math textbook, there are several geometric formulas that she needed to study for her Milestones Exam. The first formula she needed to know was the formula for the surface area of a rectangular prism which was written in which is width, is length, and stands for height. The next three formulas she needs to know all pertain to volume. A cylinder is listed as , a cone is written , and a sphere can be calculated by using the formula , where for each formula h stands for height, andr is the radius. Of the formulas listed, Millie notices that one of the formulas is linear while the other three are nonlinear.
A. Which of the formulas that Millie needs to know is linear?______
B. Explain how you know the formula above would produce a liner equation. ______
C. Explain what makes the three nonlinear equations different from the linear equation. How could you test to see if they are linear or nonlinear?
______
21. Which equation is the same as written in slope-intercept form?
a. b.
c. d.
22. Determine which graph represents the equation .
a. b.
c. d.
23. Choose the one bestanswer in regards to the graph below.
24. Your house is infested with roaches and you need to hire a pest control company to eradicate the insects from your property. The first company you call for a price quote is Victor’s Varmint Control which charges $50 to become a member and then $36 for each visit. Parker Pest Removal is more expensive per visit at $44, but their membership cost is only $10. The third and final company you called went out of business since the amount of money being made by the company was less than the amount the company spent on pest removal chemicals.
A. Set up an equation for each pest company, where x is the number of visits from each company, and y represents how much money you would pay for each company.
Name______Date______Teacher______Group______
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Name______Date______Teacher______Group______
B. Both companies tell you that you will need six visits to completely kill all of the cockroaches and their eggs. How much money would you save if you went with the cheaper company and schedule six visits?
______
C. In order to get the best deal possible determine, how many visits it would take for the cost of both companies to be the same?
______
25. Barney solved the multi-step equation below and determined the equation did not have a solution.
A. What did Barney do wrong? At which step did Barney make a mistake?
______
B. What is the correct answer? Check your work to prove your answer is correct.
______
26. Which of the following answer choices could represent the graph shown below?
a.
c. d.
Main Terms and Concepts