1. Chapter 3
Linear Equations

2. 3-1: Graphing Linear Equations
Standard Form:
Constant:
Coefficient:
Label the parts of the equation:
5x + 7y = 4

3. Page 153
Ex 1: Determine whether each equation is a linear equation. Write the equation in standard form.
y = 4 – 3x Guided Practice 1a.
b. 6x – xy = 4 Guided Practice 1b.

4. x-intercept: y-intercept: Page 154
Ex 2: Find the x and y intercepts on the line graphed at the right
Guided Practice 2a: Find the x and y intercepts on the line graphed at the right

5. Draining a Pool
Time (h)
Volume (gal) X Y
10,080 2
8,640 6
5,760 10
2,880 12
1,440 14
Page 155
Ex 3:
Find the x and y-intercepts of the graph of the function
Describe what the intercepts mean in this situation
Draw graph here:

6. Page 155
Guided Practice 3A: The table shows the function relating the distance to an amusement park in miles and the time in hours the Torrez family has driven. Find the x- and y-intercepts. Describe what they intercepts mean in this situation.
Time (h)
Distance (mi)
248 1
186 2
124 3 62 4

7. y = 2
x = 2

8. Domain:
Range:
(Page 155)
Ex 4: Graph 2x + 4y = 16 by using the x- and y-intercepts.

9. (Page 155)
Guided Practice 4A: -x + 2y = 3
Guided Practice 4B: y = -x -5

10. Page 156 Ex 5: Graph X 1/3x+2 Y (x, Y) -3 1/3(-3) + 2 1 (-3, 1)
1/3(0) + 2 2
(0, 2) 3
1/3(3) + 2
(3, 3) 6
1/3(6) + 2 4
(6, 4)

11. Page 156
Guided Practice: Graph each equation by making a table.
5A. 2x – y = B. x = 3
HW: , (odd), 42, 50, (odd), 58

12. 3-2: Solving Linear Equations by Graphing
Page 161
Linear Function:
Root
Zeros

13. Page 162
Ex 1: Solve each equation
0 = 1/3x – b. 3x + 1 = -2 (Solve by graphing – use table)
Guided Practice
1A. 0 = 2/5x B x + 3 = 0 (Solve by graphing)

14. Page
Ex 2: Solve each equation
3x +7 = 3x b. 2x – 4 = 2x – 6 (Solve by graphing)
Guided Practice:
2A. 4x + 3 = 4x – B. 2 – 3x = 6 – 3x (Solve by graphing)

15. Ex 3: Estimating by Graphing
Page 163
Ex 3: Estimating by Graphing
Emily is going to a local carnival. The function m = 20 – 0.75r represents the amount of money, m, she has left after r, rides. Find the zero of this function. Describe what this value means in this context. R
M = 20 – 0.75r m
(r,m)

16. Page 163
Guided Practice 3
Antoine’s class is selling candy to raise money for a class trip. They paid $45 for the candy, and they are selling each candy bar for $ The function y = 1.50x – 45 represents their profit, y, when they sell x candy bars. Find the zero and describe what it means in the context of this situation. X
Y = 1.50x - 45 y
(x,y)
HW: pg : (odd), 36, 44-46, 48-49

17. Rise
Run
1. Original set up:
2. Move books to make ramp steeper:
Add more books:
4. #41 from page 177:
5. #42 from page 177:

18. 3-3: Rate of Change and Slope
Page 170
Rate of Change:
Change in y
Change in x X: Y:
Positive rate of change:
Negative rate of change:

19. Number of Computer Games
Ex 1: Use the table to find the rate of change. Then explain its meaning.
Guided Practice: The table shows how the tiled surface area
changes with the number of floor tiles.
Find the rate of change
Explain the meaning of the rate of change
Number of Computer Games
Total Cost ($) X Y 2 78 4
156 6
234
Number of Floor Tiles
Area of Tiled surface X Y 3 48 6 96 9
144

20. Page 171
Ex 2: The graph shows the number of people who visited U.S. them parks in recent years.
Find the rates of change for and \
b. Explain the meaning of the rate of change in each case.
c. How are the different rates of change shown on the graph?
Guided Practice: Refer to the graph above. Without calculating, find the 2-year period that has the least rate of change. Then calculate to verify your answer.

21. Page 172
Ex 3: Determine whether each function is linear. Explain.
Guided Practice 3A: Guided Practice 3B: X Y 1 -6 4 -8 7
-10 10
-12 13
-14 X Y -3 10 -1 12 1 16 3 18 5 22 X Y -3 11 -2 15 -1 19 1 23 2 27 X Y 12 -4 9 1 6 3 11 16

22. Slope (m) =
Slope is a type of _______________________
Slope describes _________________________________
The greater the ______________________________ of the slope, the steeper the line.
m = change in y or ___________
change in x

23. Slope can be:
_________________ _________________

24. Ex 5: Find the slope of the line that passes through ( -2, 4 ) ad ( -2, -3 ).
Guided practice 5A:
Find the slope of the line that passes through ( 6, 3 ) and ( 6, 7 ).
HW: , (odd), 42-49, 52

25. Page 174
Ex 6: Find the value of r so that the line through ( 1, 4 ) and ( -5, r ) has a slope of 1/3
Guided Practice: Find the value of r so the line that passes through each pair of points has the given slope.
6A. ( -2, 6 ), ( r, -4 ); m = -5 GP 6B: ( r, -6 ), (5, -8 ); m = -8

26. 3-4: Direct Variation Direct variation:
Page 180
Direct variation:
Constant of variation/Constant of proportionality =
Ex 1: Name the constant of variation for each equation. Then find the slope of the line that passes through each pair of points
a b.

27. Page 180
Guided Practice
1a: Name the constant of variation for y = 1/4x. Then fid the slope of the line that passes through ( 0, 0) ad ( 4, 1 ).
1B: Name the constant of variation for y = -2x. Then find the slope of the line that passes through ( 0,0) ad ( 1, -2 ).

28. Page 181
Ex 2: Graph y = -6x
***The graph of a direct variation will always pass through the origin (0,0)
Guided Practice:
2A. y = 6x 2B. y = 2/3x 2D. y = -3/4x

29. If the relationship between the values of y and x can be described by a direct variation equation, then we say that y varies directly as x.
Ex 3: Suppose y varies directly as x, ad y = 72 when x = 8
Write a direct variation equation that relates x and y
Use the direct variation equation to find x when y = 63
Guided Practice 3: Suppose y varies directly as x, and y = 98 when x = 14. Write a direct variation equation that relates x and y. Then find y when x = -4

30. y = kx
d = rt
Ex 4: The distance a jet travels varies directly as the umber of hours it flies. A jet traveled 3420 miles in 6 hours.
Write a direct variation equation for the distance d flown in time t.
Graph the equation.
c. Estimate how many hours it will take for an
airliner to fly 6500 miles

31. Guided Practice 4: A hot-air balloon's height varies directly as the balloon’s ascent time in minutes.
Write a direct variation for the distance d ascended in time t.
Graph the equation
Estimate how many minutes it would take to ascend 2100 feet
About how many minutes would it take to ascend 3500 feet?
HW: Page , 10-33

32. 3-5: Arithmetic Sequences as Linear Functions
Terms of the sequence:
Distance (m)
400
800
1200
1600
2000
Time (min:sec)
1:32
3:04
4:36
6:08
7:40

33. Arithmetic Sequence: *
Common difference (d):
Increasing:
Decreasing:
… means:

34. Ex 1: Determine whether each sequence is an arithmetic sequence
Ex 1: Determine whether each sequence is an arithmetic sequence. Explain.
-4, -2, 0, 2 b. ½, 5/8, ¾, 13/16
Guided Practice
1A. -26, -22, -18, B. 1, 4, 9, 25
Ex 2: Find the next three terms of the arithmetic sequence 15, 9, 3, -3
Guided Practice: Find the next four terms of the arithmetic sequence 9.5, 11, 12.5, 14

35. a: d: n: y: :

36. Ex 3:
Write a equation for the nth term of the arithmetic sequence -12, -8, -4, 0, …
Find the 9th term of the sequence.
Graph the first five terms of the sequence
Which term of the sequence is 32?

37. Guided Practice: Consider the arithmetic sequence 3, -10, -23, -36, …
3A: Write an equation for the nth term of the sequence
3B: Find the 15th term in the sequence
3C. Graph the first five terms of the sequence
3D. Which term of the sequence is -114

38. Ex 4: Marisol is mailing invitations to her quinceanera
Ex 4: Marisol is mailing invitations to her quinceanera. The arithmetic sequence, $0.42, $0.84, $1.26, $1.68, … represents the cost of postage.
Write a function to represent this sequence
B. Graph the function
Guided Practice: The chart below shows the length of Marin’s long jumps.
Write a function to represent this arithmetic sequence.
Then graph the function
Jump 1 2 3 4
Length (ft) 8
9.5 11
12.5

39. 3-6: Proportional and Nonproportional Relationships
An equation is proportional when _________________________________________________
Ex 1: Marcos is a personal trainer at a gym. In addition to his salary, he receives a bonus for each client he sees.
Graph the data. What can you deduce from the pattern about the relationship between the number of clients and the bonus pay?
Write an equation to describe this relationship
Use this equation to predict the amount of Marcos’ bonus if he sees 8 clients

40. Write an equation to describe this relationship.
Guided Practice: A professional soccer team is donating money to a local charity for each goal they score.
Graph the data. What ca you deduce from the pattern about the pattern about the relationship between the number of goals and the money donated?
Write an equation to describe this relationship.
use this equation to predict how much money will be donated for 12 goals
Number of Clients 1 2 3 4 5
Bonus Pay ($) 45 90
135
180
225

41. Nonproportional Relationship:
Ex 2: Write an equation in function notation for the graph
Guided Practice:
2A. Write an equation in function notation for the relation shown in the table
2B. Write an equation in function notation for the graph
HW: Page , 7, 9-15, 17-35 X 1 2 3 4 Y