1. Formulas for Linear Functions
Lesson 1.4

2. What Do You Know about These Forms of Linear Equations?
Slope Intercept form
Standard form
Slope-Point form (h,k) a point on the line m = the slope
Two Intercept form

3. Slope and Y-Intercept Consider y = m * x + b
The m and b are called parameters
they affect the appearance of the graph
The m is the slope
m > 0 line is up to the right
m < 0 line is down to the right
m = 0 horizontal line
|m| large very steep line

4. Slope and Y-Intercept Considering y = m * x + b
The b is the y-intercept
Where on the y-axis, the line intersects
On your calculator
Go to Y= screen
Enter at Y1 (2/3) * x + 5
Predict what the graph will look like before you specify F2, 6 for standard zoom

5. Slope and Y-Intercept The function y = (2/3) * x + 5
Slope = 2/3 (up to the right)
Y-intercept = 5 •

6. Slope
When slope =
Try y = -7x – 3 (predict the results before you graph)

7. Graphing a Function y = -7x – 3
Do the slope and y-intercept agree with your prediction?
y-intercept = -3

8. Creating a Function from a Table
Determine slope by using x y 3 7 4
8.5 5 10 6
11.5
Answer:

9. Creating a Function from a Table
Now we know slope m = 3/2
Use this and one of the points to determine y-intercept, b
Substitute an ordered pair into y = (3/2)x + b x y 3 7 4
8.5 5 10 6
11.5

10. Creating a Function from a Table
Double check results
Substitute a different ordered pair into the formula
Should give a true statement x y 3 7 4
8.5 5 10 6
11.5

11. Finding Formulas from Verbal Description
Read exercise 40, pg 34 of text
Profit y = ___ x + ______ where x is number of patrons?
What does the slope mean?
What does the y-intercept mean?
How many patrons are needed to start making money?
How could you represent patrons p = ____ x + _____ where x is the amount of profit?

12. Using a Graph to Find a Formula
Given a graph with two points
Use the points to determine slope, m
Substitute (x,y) from one of points to find b
Answer:
(2,7) •
(8, 3.4) •

13. Assignment Lesson 1.4 Page 32
Exercises 1 – 9, 11, 13, 15, 17, 19, 21, 23, 29, 37, 41