Graphing Linear Equations

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

The Cartesian Coordinate System and Linear Equations in Two Variables

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).

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.

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.

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.

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.

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

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

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.

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.