1. Algebra 1
Section 6.4

2. Graphing Linear Equations
We can make a table of ordered pairs.
We can use the x- and y- intercepts.
We can use the slope-intercept form of the line.

3. Writing a Linear Equation
We can write the equation of a line if given the following information:
slope and y-intercept
slope and a point on the line

4. Writing a Linear Equation
We can write the equation of a line if given the following information:
two points on the line
the graph of the line

5. Example 1 Given: slope: ⅔ y-intercept: (0, -5) 2 3 y = m x + -5 b
y = x – 5 2 3

6. Example 2 Given: slope: 3 point: (1, 5) y = m x + b y = 3x + 2 5 = 3
(1) + b
5 = 3 + b
b = 2

7. Example 4 Given: slope: 0 point: (1, -6) y = m x + b y = 0x – 6 y = -6
-6 =
(1) + b
-6 = 0 + b
b = -6

8. Example 5 Strategy: First, find the slope m. Next, find b.
Then, use m and b to write the equation in slope-intercept form. 5 3 – 14 3

9. Example 5
y = m
x + b 5 3 – 14 3
y =
x +
The second point, (4, -2), can be used to check your work since it must be a solution to the equation.

10. Example 6 The strategy will remain the same as before.
The slope of the line is undefined; therefore, the line must be vertical.
x = 7

11. Example 7 Choose two convenient points from the graph.
Use the slope formula to determine the estimated rate of growth.
people
year
m = 500

12. Example 7
Use one of the points, (2010, 56,500), and the slope to find b.
b = -948,500

13. Example 7
Use the slope and b to write the equation in slope- intercept form.
y = 500x – 948,500

14. Example 7
Rewrite the equation showing population as a function of time.
P(t) = 500t – 948,500

15. Models
In Example 7, the function acts as a model of population growth.
It may be useful for years close to the data, but making predictions for faraway times often causes errors.

16. Homework: pp