1. 3-5 Warm Up Problem of the Day Lesson Presentation
Equations, Tables, and Graphs
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
For each function, find the value of y for x = 0, x = 4, and x = –5.
1. y = 6x – 3
2. y = 3.8x – 12
3. y = 1.6x + 5.9
–3, 21, –33
–12, 3.2, –31
5.9, 12.3, –2.1

3. Problem of the Day
You buy two fruit baskets. Each basket contains three bunches of bananas. Each bunch contains five bananas. How many bananas do you have? 30

4. Learn to generate different representations of the same data.

5. An equation shows how the variables are related.
Additional Example 1: Using Equations to Generate Different Representations of Data
The height h of an airplane s seconds from take-off is h = 12s. Make a table and sketch a graph of the equation.
Equation
h = 12s
An equation shows how the variables are related.
The number of seconds s is the input value. The depth d is the output value.
Helpful Hint

6. Additional Example 1 Continued
Table
Graph h 50 40 30 20 10 1 2 3 4 5 s s h 1 12 2 24 3 36
A table identifies values that make the function true.
A graph is a visual image of the values in the table.

7. An equation shows how the variables are related.
Check It Out: Example 1
The height h of a helicopter s seconds from take-off is h = 15s. Make a table and sketch a graph of the equation.
Equation
h = 15s
An equation shows how the variables are related.

8. Check It Out: Example 1 Continued
Table
Graph h 75 60 45 30 15 1 2 3 4 5 s s h 1 15 2 30 3 45 4 60
A table identifies values that make the function true.
A graph is a visual image of the values in the table.

9. Additional Example 2: Using Tables to Generate Different Representations of Data
Use the table to make a graph and to write an equation. x y –1 1 2 3
Look for a pattern in the values:
0 = 1 – 1
Each value of y is the value of x minus 1.
1 = 2 – 1
2 = 3 – 1

10. Additional Example 2 Continued
Use the table to make a graph and to write an equation. x y –2 –4 2 4 x y –1 1 2 3
y = x – 1

11. Check It Out: Example 2
Use the table to make a graph and to write an equation. x y 3 1 4 2 5 6
Look for a pattern in the values:
4 = 1 + 3
Each value of y is the value of x plus 3.
5 = 2 + 3
6 = 3 + 3

12. Check It Out: Example 2 Continued
Use the table to make a graph and to write an equation. x y 3 1 4 2 5 6
y = x + 3

13. Use the graph to make a table and to write an equation.
Additional Example 3: Using Graphs to Generate Different Representations of Data
Use the graph to make a table and to write an equation. t d –4 –8 4 8
Look for a pattern in the values:
4 = 2 • 1 + 2
6 = 2 • 2 + 2
8 = 2 • 3 + 2

14. Additional Example 3 Continued
Use the graph to make a table and to write an equation.
Each value of d is 2 times the value of t plus 2. t d 2 1 4 6 3 8
d = 2t + 2

15. Use the graph to make a table and to write an equation.
Check It Out: Example 3
Use the graph to make a table and to write an equation. t d –2 –4 2 4 8 –8
Look for a pattern in the values:
2 = 3 • 1 – 1
5 = 3 • 2 – 1
8 = 3 • 3 – 1

16. Check It Out: Example 3 Continued
Use the graph to make a table and to write an equation.
Each value of d is 3 times the value of t minus 1. t d –1 1 2 5 3 8
d = 3t – 1

17. 1. Make a table and sketch the graph of w = –2x + 3. x w 3 1 2 -1 -3
Lesson Quiz: Part I
1. Make a table and sketch the graph of w = –2x + 3. x w –2 –4 2 4 x w 3 1 2 -1 -3

18. 2. Use the table to sketch a graph and write an equation. y = –x x y
Lesson Quiz: Part II
2. Use the table to sketch a graph and write an equation.
y = –x x y –2 –4 2 4 x y -1 1 2 -2

19. Lesson Quiz: Part III
3. Use the graph to make a table and to write an equation.
y = 4x + 1 x y 2 9 1 5 –1 –3