Graphing linear equations

1. Graphing Linear Equations

2. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: , Point-Slope Form: , and Standard Form: . Each form allows for quick and easy ways to graph the line they represent.   Forms of Linear Equations

3. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form ( ). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and Repeat. In this way, we can create a table of ordered pairs and plot them on the coordinate plane .   Make a Table

4. Consider the equation .   Make a Table -2 2 -2 2       (-2,1 ) =1 =2 (0, 2) =3 (2, 3)

5. Another method for graphing lines when an equation is in slope-intercept form is as follows: Plot the y-intercept on the coordinate plane; that's the point (0, b ). Use the slope to find another point (and repeat). Draw a line through the points . Use the slope and intercept

6. Plot the y-intercept Use the slope to find another point (and repeat). Draw a line through the points. Consider the equation .   Use the slope and intercept (0, b ) = (0, 7 ) From the intercept, move down 5 and right 4 (or up 5 and left 4).

7. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Plot the point ( , ). Use the slope to find another point (and repeat). Draw a line through the points.   Use a point and the slope

8. Plot the point ( , ) Use the slope to find another point (and repeat). Draw a line through the points.   Consider the equation .   Use a point and the slope ( , ) = (-3, 2)   From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.

9. This method is used when the line is in Standard Form ( ). The x -intercept is easily calculated by setting y to 0 and solving for . The y -intercept is calculated by setting to zero and solving for . Plot the two intercepts and draw a line through them .   Use the Intercepts

10. Set and solve for . Set and solve for . Draw a line through the points.   Consider the equation .   Use the Intercepts ;   ;