1. Graphing Linear Equations

2. Chapter Sections
7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables
7.2 – Graphing Linear Equations
7.3 – Slope of a Line
7.4 – Slope-Intercept and Point-Slope Forms of a Linear Equation
7.5 – Graphing Linear Inequalities
7.6 – Functions
Chapter 1 Outline

3. The Cartesian Coordinate System and Linear Equations in Two Variables

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, 5).
The x-coordinate is 3 and the y-coordinate is 5.

8. Plotting Points Plot the point (3, 5).
Then move 5 places up.
Plot the point (3, 5).
The x-coordinate is 3 and the y-coordinate is 5.

9. Plotting Points (3, 5) Plot the point (3, 5).
The x-coordinate is 3 and the y-coordinate is 5.

10. Linear Equations Examples: 4x – 3y = 12 y = 5x + 3
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
y = 5x + 3

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 coordinates satisfy the equation.
A set of points that are on a line are collinear.
The points (–1, 4), (1, 1) and (4, –3) are collinear.