1. Graphing Linear Equations Chapter 7

2. Angel, Elementary Algebra, 7ed 2 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 7.5 – Graphing Linear Inequalities 7.6 – Functions Chapter Sections

3. § 7.1 The Cartesian Coordinate System and Linear Equations in Two Variables

4. Angel, Elementary Algebra, 7ed 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 (1596-1650).

5. Angel, Elementary Algebra, 7ed 5 Definitions The two intersecting axis form four quadrants, numbered I through IV. IVIII III The horizontal axis is called the x-axis. The vertical axis is called the y-axis. x y

6. Angel, Elementary Algebra, 7ed 6 Definitions The point of intersection of the two axes is called the origin. Origin, or the value of the x and the value of the y The coordinates, or the value of the x and the value of the y determines the point. This is also called an ordered pair. x y (0, 0)

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

8. Angel, Elementary Algebra, 7ed 8 Plotting Points Plot the point (3, –4). The x-coordinate is 3 and the y-coordinate is –4. Then move 4 places down.

9. Angel, Elementary Algebra, 7ed 9 Plotting Points Plot the point (3, –4). The x-coordinate is 3 and the y-coordinate is –4. (3, -4)

10. Angel, Elementary Algebra, 7ed 10 Linear Equations 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. of an equation. This is called the standard form of an equation. Examples: 4x – 3y = 12 x + 2y = – 35

11. Angel, Elementary Algebra, 7ed 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. Angel, Elementary Algebra, 7ed 12 Graphing A graph of an equation is an illustration of a set of points whose coordinates satisfy 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.