1. introducing Section 4: Linear Functions Topics 1-4
Grab a set of interactive notes.
Try “Let’s Recall”
Problems 1 & 2 (Page 2 of notes)

2. TARGET
Algebra

3. Arithmetic Sequence Sequence
A sequence is a set of things (usually numbers) that are in order.

4. Arithmetic Sequence
In an Arithmetic Sequence the difference between one term and the next is a constant.
In other words, we just add the same value each time ... infinitely.
In General: we could write an arithmetic sequence like this:
{a, a+d, a+2d, a+3d, ... }
where:
a is the first term, and
d is the difference between the terms
(called the "common difference")

5. Arithmetic Sequence

6. Arithmetic Sequence Rule
We can write an Arithmetic Sequence as a rule:
formula(n) = a + d(n-1)
(We use "n-1" because d is not used in the 1st term).

7. Arithmetic Sequence
Example: Write the Rule, and calculate the 4th term for: 3, 8, 13, 18, 23, 28, 33, 38, ...
This sequence has a difference of 5 between each number.
The values of a and d are:
a = 3 (the first term)
d = 5 (the "common difference")

8. Arithmetic Sequence The Rule can be calculated:
formula(n) = a + d(n-1)
= 3 + 5(n-1)
= 3 + 5(4 – 1)
= 3+5(3)
So, the 4th term is:
f(4) = 3+15 = 18

9. Arithmetic Sequence
What is the twentieth term of the arithmetic sequence 21, 18, 15, 12, ... ?
This sequence is descending, so has a difference of -3 between each pair of numbers. The values of a and d are: • a = 21 (the first term) • d = -3 (the "common difference") The Rule can be calculated: f(n) = a + d(n-1)
The Rule can be calculated: xn = a + d(n-1) = (n-1) 
So, the 20th term is: x20 = × 20 = = -36

10. Arithmetic Sequence
What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15, ... ?
This sequence has a difference of 4 between each pair of numbers. The values of a and d are: a = 3 (the first term) d = 4 (the "common difference") The Rule can be calculated: xn = a + d(n-1) = 3 + 4(n-1)  So, the 50th term is: x50 = 4 × = = 199

11. Section 4: Linear Equations Topic 1 - 4
Let’s recall:
1. Find the x-intercept, y-intercept
and Graph the line
4x + 2y = 8
2. Solve for y
6y – 3 x = 12

12. Slope-Intercept Form
You have graphed a line by knowing two points on the line.
Another tool for your Mathematical Tool Box is to learn how to use the slope of the line and the point that contains the y-intercept to graph a line.

13. Graph the line given the slope and y-intercept.
Step 1 Identify the y-intercept
this is your base Constant y
Rise • •
Step 2 Identify your slope =
“work” the slope from the y-intercept, plot your point, then “work” the slope again to get your 3rd point. •
Run
Step 3 Draw the line through the three points.

14. Graph the line given the slope and y-intercept.
Step 1 Identify the y-intercept 4  Plot (0, 4).
Rise = –2 y • • •
Step 2 Identify Slope =
Count 2 units down & 5 units over from base (0, 4)  plot point. •
Run = 5
Step 3 Draw the line through the three points.

15. Graph the line given the slope and y-intercept.
slope = 2, y-intercept = –3
Step 1
Step 2
Step 3

16. Graph each line given the slope and y-intercept.
slope = , y-intercept = 1
Step 1
Step 2
Step 3.

17. b= base = y-intercept
m= slope
Any linear equation can be written in slope-intercept form by solving for y and simplifying.
In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

18. Ch 4 Lesson 6
Slope-Intercept Form

19. Write the equation that describes the line In slope-intercept form.
Given:
slope = ; y-intercept = 4
y = mx + b
Substitute the given values for m and b.
Simply if necessary.

20. Write the equation that describes the line in slope-intercept form.
Given:
slope = –9; y-intercept =
Substitute the given values for m and b.
y = mx + b
Simply if necessary.

21. Write the equation that describes the line in slope-intercept form.
Step 1 Find the y-intercept.
b =
Step 2 Find the slope.
m =

22. Write the equation that describes each line in slope-intercept form.
slope = −12, y-intercept =
y = mx + b
Substitute the given values for m and b.
Simplify if necessary.

23. Write the equation that describes each line in slope-intercept form.
slope = 1, y-intercept = 0
Substitute the given values for m and b.
y = mx + b

24. Graph the line described by the equation.
y = 3x – 1
slope: m =
y-intercept: b =

25. Write the equation in slope-intercept form
Write the equation in slope-intercept form. Then graph the line described by the equation.
2y + 3x = 6
Write the equation in slope-intercept form by solving for y.

26. Write the equation in slope-intercept form
Write the equation in slope-intercept form. Then graph the line described by the equation.

27. Write the equation in slope-intercept form
Write the equation in slope-intercept form. Then graph the line described by the equation.
Write the equation in slope-intercept form.
Then graph the line described by the equation.
6x + 2y = 10

28. Write the equation in slope-intercept form
Write the equation in slope-intercept form. Then graph the line described by the equation.
y = –4

29. Write the equation that describes each line in slope-intercept form.
Exit Slip
1. slope = 3, y-intercept = –2
2. slope = 0, y-intercept =
3. slope = , (0, 4) is on the line.
4. Write the equation of the graph in slope-intercept form

30. Rate of Change = Slope of a Line
The Slope Formula
Ch 4 Lesson 3
Rate of Change and Slope
Rate of Change = Slope of a Line
You can find the slope of a line from any two ordered pairs.
The ordered pairs can be given to you, or you might need to read them from a table or graph.

31. Rate of Change and Slope
The Slope Formula
Ch 4 Lesson 3
Rate of Change and Slope

32. The Slope Formula
Rate of Change

33. Rate of Change and Slope
The Slope Formula
Ch 4 Lesson 3
Rate of Change and Slope
Rate of Change

34. Rate of Change
A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

35. Rate of Change Real Life Application
The table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?
Step 1 Identify the dependent and independent variables.
dependent: temperature independent: month

36. Rate of Change Example 1 Continued Step 2 Find the rates of change.
2 to 3
3 to 5
5 to 7
7 to 8
The temperature increased at the greatest rate from month 5 to month 7.

37. Rate of Change Name each of the following.
The table shows the number of bikes made by a company for certain years. Find the rate of change for each time period. During which time period did the number of bikes increase at the fastest rate?
1 to 2: 3; 2 to 5: 4; 5 to 7: 0; 7 to 11: 3.5;
from years 2 to 5

38. Homework:
Section 4
Topic 1 – 4 Study Guide