1. Algebra 1
Section 6.1

2. Graphing
By recognizing key characteristics of a function, you can quickly determine the shape and location of its graph.

3. Linear Functions f(x) = 2x + 7 y = 2x + 7
These are called linear functions or linear equations because all the points that satisfy them form a straight line.

4. Example 1 Graph {(x, y) | y = x + 5} x x + 5 (x, y) -2 -1 1 21 2
(-2) + 5 = 3
(-1) + 5 = 4
(0) + 5 = 5
(1) + 5 = 6
(2) + 5 = 7
(-2, 3)
(-1, 4)
(0, 5)
(1, 6)
(2, 7)

5. Example 1 y x

6. Standard Form
The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers.
Several different standard-form equations are possible for the same linear function.

7. Standard Form
If a linear equation in standard form contains fractional or decimal coefficients, multiply each term so that A, B, and C become integers.
It is also common for A to be nonnegative.

8. Example 2 5 f(x) = - x + 2 7 5 y = - x + 2 7 5 x + y = 2 7

9. Example 3
Graph x + 3y = 4.
Solve for y:
3y = -x + 4
y = 4 3 x

10. Example 3 y = - + 4 3 x Make a table to find ordered pairs.
(0, ), (1, 1), (4, 0)
Graph the ordered pairs and connect with a straight line. 4 3

11. Graphing a Linear Equation
Solve the linear equation for y.
Make a table of at least three ordered pairs using convenient values for x.

12. Graphing a Linear Equation
Graph the ordered pairs on a Cartesian plane.
Connect the points with a straight line.

13. Definitions
The y-intercept is the point where the graph intersects the y-axis.
The x-intercept is the point where the graph intersects the x-axis.

14. Intercepts
A line’s intercepts can be found from the equation without graphing.
The y-intercept always has zero for its x-coordinate.
The x-intercept always has zero for its y-coordinate.

15. Example 4
2x + y = 6
To find the x-intercept, substitute 0 for y and solve for x.
2x + 0 = 6
2x = 6
x = 3

16. Example 4
2x + y = 6
To find the y-intercept, substitute 0 for x and solve for y.
2(0) + y = 6
0 + y = 6
y = 6

17. Example 4 2x + y = 6 Plot each intercept: The x-intercept is (3, 0).
The y-intercept is (0, 6).
Graph the line.
Check by using a third point.

18. Horizontal and Vertical Lines
An equation of the form y = c is a horizontal line.
An equation of the form x = c is a vertical line.

19. Example 5 y = -2 x = 3 y y = -2 regardless of the value chosen for x.
x = 3 regardless of the value chosen for y. x

20. Example 5 y = -2 is a function; it passes the vertical line test.
x = 3 is not a function; it fails the vertical line test.

21. Homework: pp