Section 2.1: Review
Name: Period:
1. A proportional constant of relates the number of inches a flower grows to the number of weeks since being planted.
a. State the independent and dependent variables.
b. Complete the table.
c. Write an equation that represents this relationship and use the equation to predict how tall the flower will be after 8 weeks.
d. Can the flower continue to grow in this manner forever?
e. Is this situation proportional? Explain why or why not using your table of values and equation.
2. Laura has a job delivering newspapers. Laura gets paid $100 dollars for delivering 200 papers.
a. State the independent and dependent variables.
b. Find the unit rate. State what it describes.
c. Complete the table of values and graph for this situation. Label each axis and label your line Laura. Should your points be connected? Explain why or why not.
x: y:
100
100 150
d. Write an equation for this situation.
3. Kali also has a job delivering newspapers. She gets paid $20 for expenses and then $140 for delivering 350 papers.
a. Find the unit rate for this situation. State what it describes.
x: 1 3 9 30
y: 2
40 80 120 160 200 240 280
20 40 60 80 100 120 140 160 180
Stage 1 Stage 2 Stage 3 c. Write an equation for this situation.
d. Which situation, Laura or Kali, represents a non-proportional relationship? Justify using your graph and equations.
e. What does the point (200, 100) represent in the context?
4. Nayala bought 5 pounds of mangos for $6.25.
a. What is the price per pound for the mangos that she bought?
b. Which line on the graph, A, B, or C, represents Nayala’s situation?
5. Emma is putting together an order for sugar, flour, and salt for her restaurant pantry. The graph shows the cost to buy pounds of sugar and flour. One line shows the cost of buying pounds of flour and the other line shows the cost of buying pounds of sugar.
a. From the graph, which ingredient costs more to buy per pound? Justify your answer.
b. The cost to buy salt by the pound is less than sugar and flour. Draw a possible line that could represent the cost to buy x pounds of salt.
6. Write two different rules that describe the pattern where is the stage number and is the total number of blocks. Explain how your rules connect to the pattern.
Rule 1: Rule 2:
Sugar
Stage 1 Stage 2 Stage 3 Stage 4 a. Simplify both rules. What do you notice?
b. How many blocks are in stage 0? How is this value represented in the simplified rule?
c. Use your rule to find the number of blocks in the 50th stage.
d. Which stage has 582 blocks?
7. Use the pattern to complete the following.
a. Draw stage 4.
b. How many new blocks are added to the pattern from one stage to the next?
c.
d. Create a graph of this data. Show the unit rate on your graph.
e. What is the simplified form of the equation that gives the number of blocks, for any stage Where do you see the different parts of the equation in the geometric model, table, and graph?
Equation:
Model Table Graph
Stage (s) # of Blocks (b) 1
2 3 4 Complete the table. State the first difference
f. If the equation changed to , how would your geometric model change? How would your table change? How would your graph change?
Model Table Graph
8. For each of the representations given below, identify the unit rate and initial value or y-intercept.
e.
a. The local community center charges a monthly fee of $15 to use their facilities plus $2 per visit.
unit rate:
initial value:
b. unit rate:
initial value:
x y
2 10
3 5
4 0
c. unit rate:
y-intercept:
d. unit rate:
y-intercept: Stage 1 Stage 2 Stage 3
unit rate:
Directions: Complete the remaining representations that are not given. When needed, label the columns in the table and axes on the graph.
9.
Context
The number of students currently enrolled at Discovery Place Preschool is 24. Enrollment is increasing by 6 students each year. Consider the relationship between the number of years from now and the number of students enrolled.
Table
independent variable: dependent variable:
x: y:
2 4 6
Graph
Should your points be connected on your graph? Explain why or why not.
Equation
Is this situation proportional? Explain why or why not using the context.
What is the unit rate? What does the unit rate represent in the context?
a. What is the y-intercept of your graph? How is the y-intercept shown in the equation?
b. What does the y-intercept represent in the context?
c. How would you change the context so that the relationship between number of years and number of students enrolled is ?
d. What would happen to the graph if the maximum enrollment at the school was 72?
e. How would the graph of the line change if enrollment increased to 10 students each year?
2 4 6 8 10 12 14
12 24 36 48 60 72 84
