Graphing Linear Equations From the beginning

What is a Linear Equation? A linear equation is an equation whose graph is a LINE. Linear Not Linear

What is a Linear Equation? A solution to the equation is any ordered pair (x, y) that makes the equation true. If we were to plot all these ordered pairs on a graph, we would be graphing a line. The equations we will be graphing have two variables, x and y. For example, The ordered pair (3, 2) is a solution since,

The x - values are picked by YOU! Complete the table by inputting the x - values and calculating the corresponding y - values. Graphing a Linear Equation How do we graph linear equations? Let’s try this one: y = 3x – 2 Make a Table of values xy –2 – y = 3(–2) – 2 = –8 y = 3(–1) – 2 = –5 y = 3(0) – 2 = –2 y = 3(2) – 2 = 4 y = 3(1) – 2 = 1 –8 –5 –2 1 4

Graphing a Linear Equation How about another one! Let’s try x – 2y = 5. First Step: Write y as a function of x x – 2y = 5 –2y = 5 – x

Graphing a Linear Equation How about another one! Let’s try x – 2y = 5. Second Step: Make a Table of Values xy –2 –1 0 1 –3 –2 Take a moment and complete the chart… Click the screen when finished

Graphing Horizontal & Vertical Lines When you are asked to graph a line, and there is only ONE variable in the equation, the line will either be vertical or horizontal. For example … Graph x = 3 Since there are no y – values in this equation, x is always 3 and y can be any other real number. x = 3 Graph y = –2 Since there are no x – values in this equation, y is always – 2 and x can be any other real number. y = –2