1. Chapter 3
Graphs and Functions

2. Chapter Sections 3.1 – Graphs 3.2 – Functions
3.3 – Linear Functions: Graphs and Applications
3.4 – The Slope-Intercept Form of a Linear Equation
3.5 – The Point-Slope Form of a Linear Equation
3.6 – The Algebra of Functions
3.7 – Graphing Linear Inequalities
Chapter 1 Outline

3. § 3.1
Graphs

4. Definitions
A graph shows the relationship between two variables in an equation.
The Cartesian (rectangular) coordinate system is a grid system used to draw graphs. It is named after its developer, René Descartes ( ).

5. Definitions y II I x
III IV
The two intersecting axis form four quadrants, numbered I through IV.
The horizontal axis is called the x-axis.
The vertical axis is called the y-axis.

6. Definitions y
Origin x
(0, 0)
The point of intersection of the two axes is called the origin.
The coordinates, or the value of the x and the value of the y determines the point. This is also called an ordered pair.

7. Starting at the origin, move 3 places to the right.
Plotting Points
Starting at the origin, move 3 places to the right.
Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.

8. Plotting Points Plot the point (3, -4).
Then move 4 places down.
Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.

9. Plotting Points (3, -4) Plot the point (3, -4).
The x-coordinate is 3 and the y-coordinate is –4.

10. Linear Equations Examples: 4x – 3y = 12 x + 2y = -35
A linear equation in two variables is an equation that can be put in the form
ax + by = c
where a, b, and c are real numbers.
This is called the standard form of an equation.
Examples:
4x – 3y = 12
x + 2y = -35

11. Solutions to Equations
The solution to an equation is the ordered pair that can be substituted into the equation without changing the “validity” of the equation.
Is (3, 0) a solution to the equation 4x – 3y = 12?
4x – 3y = 12
4(3) – 3(0) = 12
12 – 0 = 12
12 = 12 
Yes, it is a solution.

12. Graphing
A graph of an equation is an illustration of the set of points whose ordered pairs are solutions to the equation.
A set of points that are in a straight line are collinear.
The points
(-1, 4), (1, 1) and (4, -3)
are collinear.

13. Graph Nonlinear Equations
Equations whose graphs are not straight lines are called nonlinear equations.
Example: Graph y = x2 – 4. Use the following values for x: -3, -2, -1, 0, 1, 2, and 3.