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Graphing Linear Equations
Linear Equations are most often expressed in one of three forms: Forms of Linear Equations
Linear Equations are most often expressed in one of three forms: Slope-Intercept Form:  𝑦=𝑚𝑥+𝑏,   Forms of Linear Equations
Linear Equations are most often expressed in one of three forms: Slope-Intercept Form:  𝑦=𝑚𝑥+𝑏, Point-Slope Form:  𝑦−𝑦1=𝑚(𝑥−𝑥1), and   Forms of Linear Equations
Linear Equations are most often expressed in one of three forms: Slope-Intercept Form:  𝑦=𝑚𝑥+𝑏, Point-Slope Form:  𝑦−𝑦1=𝑚(𝑥−𝑥1), and Standard Form:  𝐴𝑥+𝐵𝑦=𝐶.   Forms of Linear Equations
Linear Equations are most often expressed in one of three forms: Slope-Intercept Form:  𝑦=𝑚𝑥+𝑏, Point-Slope Form:  𝑦−𝑦1=𝑚(𝑥−𝑥1), and Standard Form:  𝐴𝑥+𝐵𝑦=𝐶. Each form allows for quick and easy ways to graph the line they represent.   Forms of Linear Equations
One method for graphing a line is to use a table.  This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are:   Make a Table
One method for graphing a line is to use a table.  This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable,   Make a Table
One method for graphing a line is to use a table.  This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and   Make a Table
One method for graphing a line is to use a table.  This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and Repeat.   Make a Table
One method for graphing a line is to use a table.  This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). 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
Consider the equation 𝑦=12𝑥+2.     Make a Table
Consider the equation 𝑦=12𝑥+2.     Make a Table 𝑦=12(−𝟐)+2   =1
Consider the equation 𝑦=12𝑥+2.     Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1
Consider the equation 𝑦=12𝑥+2.     Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1 𝑦=12(𝟎)+2   =2 (0, 2)
Consider the equation 𝑦=12𝑥+2.     Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1 𝑦=12(𝟎)+2   =2 (0, 2) 𝑦=12(𝟐)+2   (2, 3) =3
Another method for graphing lines when an equation is in slope-intercept form is as follows: Use the slope and intercept
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 and intercept
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). Use the slope and intercept
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
Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept  Use the slope and intercept (0, b) = (0, 7)
Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept  Use the slope to find another point (and repeat). Use the slope and intercept (0, b) = (0, 7) From the intercept, move down 5 and right 4 (or up 5 and left 4).
Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept  Use the slope to find another point (and repeat). Draw a line through the points. Use the slope and intercept (0, b) = (0, 7) From the intercept, move down 5 and right 4 (or up 5 and left 4).
This method is very similar to the slope-intercept method.  To graph a line using this method, do the following: Use a point and the slope
This method is very similar to the slope-intercept method.  To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1).   Use a point and the slope
This method is very similar to the slope-intercept method.  To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1). Use the slope to find another point (and repeat).   Use a point and the slope
This method is very similar to the slope-intercept method.  To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1). Use the slope to find another point (and repeat). Draw a line through the points.   Use a point and the slope
Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1)   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)  
Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1) Use the slope to find another point (and repeat).   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)   From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1) Use the slope to find another point (and repeat). Draw a line through the points.   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)   From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶).     Use the Intercepts
This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶).   The x-intercept is easily calculated by setting y to 0 and solving for 𝑥.   Use the Intercepts
This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶).   The x-intercept is easily calculated by setting y to 0 and solving for 𝑥. The y-intercept is calculated by setting 𝑥 to zero and solving for 𝑦.   Use the Intercepts
This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶).   The x-intercept is easily calculated by setting y to 0 and solving for 𝑥. The y-intercept is calculated by setting 𝑥 to zero and solving for 𝑦. Plot the two intercepts and draw a line through them.   Use the Intercepts
Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)  
Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥. Set 𝑥=0 and solve for 𝑦.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)   −5𝑥=−15; 𝑦=3(0,  3)  
Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥. Set 𝑥=0 and solve for 𝑦. Draw a line through the points.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)   −5𝑥=−15; 𝑦=3(0,  3)  

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GraphingLinearEquations

  • 2. Linear Equations are most often expressed in one of three forms: Forms of Linear Equations
  • 3. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: 𝑦=𝑚𝑥+𝑏,   Forms of Linear Equations
  • 4. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: 𝑦=𝑚𝑥+𝑏, Point-Slope Form: 𝑦−𝑦1=𝑚(𝑥−𝑥1), and   Forms of Linear Equations
  • 5. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: 𝑦=𝑚𝑥+𝑏, Point-Slope Form: 𝑦−𝑦1=𝑚(𝑥−𝑥1), and Standard Form: 𝐴𝑥+𝐵𝑦=𝐶.   Forms of Linear Equations
  • 6. Linear Equations are most often expressed in one of three forms: Slope-Intercept Form: 𝑦=𝑚𝑥+𝑏, Point-Slope Form: 𝑦−𝑦1=𝑚(𝑥−𝑥1), and Standard Form: 𝐴𝑥+𝐵𝑦=𝐶. Each form allows for quick and easy ways to graph the line they represent.   Forms of Linear Equations
  • 7. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are:   Make a Table
  • 8. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable,   Make a Table
  • 9. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and   Make a Table
  • 10. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). The steps are: Assign a value to the x-variable, Calculate the corresponding value for the y-coordinate, and Repeat.   Make a Table
  • 11. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=𝑚𝑥+𝑏). 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
  • 12. Consider the equation 𝑦=12𝑥+2.   Make a Table
  • 13. Consider the equation 𝑦=12𝑥+2.   Make a Table 𝑦=12(−𝟐)+2   =1
  • 14. Consider the equation 𝑦=12𝑥+2.   Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1
  • 15. Consider the equation 𝑦=12𝑥+2.   Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1 𝑦=12(𝟎)+2   =2 (0, 2)
  • 16. Consider the equation 𝑦=12𝑥+2.   Make a Table 𝑦=12(−𝟐)+2   (-2,1) =1 𝑦=12(𝟎)+2   =2 (0, 2) 𝑦=12(𝟐)+2   (2, 3) =3
  • 17. Another method for graphing lines when an equation is in slope-intercept form is as follows: Use the slope and intercept
  • 18. 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 and intercept
  • 19. 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). Use the slope and intercept
  • 20. 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
  • 21. Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept Use the slope and intercept (0, b) = (0, 7)
  • 22. Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept Use the slope to find another point (and repeat). Use the slope and intercept (0, b) = (0, 7) From the intercept, move down 5 and right 4 (or up 5 and left 4).
  • 23. Consider the equation𝑦=−54𝑥+7.   Plot the y-intercept Use the slope to find another point (and repeat). Draw a line through the points. Use the slope and intercept (0, b) = (0, 7) From the intercept, move down 5 and right 4 (or up 5 and left 4).
  • 24. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Use a point and the slope
  • 25. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1).   Use a point and the slope
  • 26. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1). Use the slope to find another point (and repeat).   Use a point and the slope
  • 27. This method is very similar to the slope-intercept method. To graph a line using this method, do the following: Plot the point (𝑥1, 𝑦1). Use the slope to find another point (and repeat). Draw a line through the points.   Use a point and the slope
  • 28. Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1)   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)  
  • 29. Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1) Use the slope to find another point (and repeat).   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)   From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
  • 30. Consider the equation𝑦−2=73(𝑥+3).   Plot the point (𝑥1, 𝑦1) Use the slope to find another point (and repeat). Draw a line through the points.   Use a point and the slope (𝑥1, 𝑦1)= (-3, 2)   From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.
  • 31. This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶).   Use the Intercepts
  • 32. This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶). The x-intercept is easily calculated by setting y to 0 and solving for 𝑥.   Use the Intercepts
  • 33. This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶). The x-intercept is easily calculated by setting y to 0 and solving for 𝑥. The y-intercept is calculated by setting 𝑥 to zero and solving for 𝑦.   Use the Intercepts
  • 34. This method is used when the line is in Standard Form (𝐴𝑥+𝐵𝑦=𝐶). The x-intercept is easily calculated by setting y to 0 and solving for 𝑥. The y-intercept is calculated by setting 𝑥 to zero and solving for 𝑦. Plot the two intercepts and draw a line through them.   Use the Intercepts
  • 35. Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)  
  • 36. Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥. Set 𝑥=0 and solve for 𝑦.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)   −5𝑥=−15; 𝑦=3(0,  3)  
  • 37. Consider the equation3𝑥−5𝑦=−15.   Set 𝑦=0 and solve for 𝑥. Set 𝑥=0 and solve for 𝑦. Draw a line through the points.   Use the Intercepts 3𝑥=−15; 𝑥=−5(−5, 0)   −5𝑥=−15; 𝑦=3(0,  3)