1. Graphing Linear Equations

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

3. What is a Linear Equation? A solution to the equation is any ordered pair (x, y) that makes this 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…

4. You get to pick the x - values! 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: y = 3x – 2 Make a table (or T-chart) xy –2 –1 0 1 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

5. Graphing a Linear Equation Now let’s try x – 2y = 5. First Step: Write y as a function of x: x – 2y = 5 –2y = – x + 5

6. Graphing a Linear Equation Let’s continue with x – 2y = 5 Second Step: Make a table xy –2 –1 0 1 –3 –2 Let’s complete the chart…

7. Find INTERCEPT points for a graph to help with graphing: To find the x -intercept: set y =0 ( x,0) To find the y -intercept: set x = 0 (0, y )

8. 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

9. The midpoint formula can be thought of as (avg of x values, avg of y values), or. …So we average the x and y values to get the midpoint. The midpoint is half-way between the two points… Midpoint formula: