Upcoming SlideShare
×

# GraphingLinearEquations

1,133 views
1,045 views

Published on

Transitions removed

Published in: Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
1,133
On SlideShare
0
From Embeds
0
Number of Embeds
523
Actions
Shares
0
37
0
Likes
0
Embeds 0
No embeds

No notes for slide

### GraphingLinearEquations

1. 1. Graphing Linear Equations<br />
2. 2. Linear Equations are most often expressed in one of three forms:<br />Forms of Linear Equations<br />
3. 3. Linear Equations are most often expressed in one of three forms:<br />Slope-Intercept Form: π¦=ππ₯+π,<br />Β <br />Forms of Linear Equations<br />
4. 4. Linear Equations are most often expressed in one of three forms:<br />Slope-Intercept Form: π¦=ππ₯+π,<br />Point-Slope Form: π¦βπ¦1=π(π₯βπ₯1), and<br />Β <br />Forms of Linear Equations<br />
5. 5. Linear Equations are most often expressed in one of three forms:<br />Slope-Intercept Form: π¦=ππ₯+π,<br />Point-Slope Form: π¦βπ¦1=π(π₯βπ₯1), and<br />Standard Form: π΄π₯+π΅π¦=πΆ.<br />Β <br />Forms of Linear Equations<br />
6. 6. Linear Equations are most often expressed in one of three forms:<br />Slope-Intercept Form: π¦=ππ₯+π,<br />Point-Slope Form: π¦βπ¦1=π(π₯βπ₯1), and<br />Standard Form: π΄π₯+π΅π¦=πΆ.<br />Each form allows for quick and easy ways to graph the line they represent.<br />Β <br />Forms of Linear Equations<br />
7. 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 (π¦=ππ₯+π).<br />The steps are:<br />Β <br />Make a Table<br />
8. 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 (π¦=ππ₯+π).<br />The steps are:<br />Assign a value to the x-variable,<br />Β <br />Make a Table<br />
9. 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 (π¦=ππ₯+π).<br />The steps are:<br />Assign a value to the x-variable,<br />Calculate the corresponding value for the y-coordinate, and<br />Β <br />Make a Table<br />
10. 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 (π¦=ππ₯+π).<br />The steps are:<br />Assign a value to the x-variable,<br />Calculate the corresponding value for the y-coordinate, and<br />Repeat.<br />Β <br />Make a Table<br />
11. 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 (π¦=ππ₯+π).<br />The steps are:<br />Assign a value to the x-variable,<br />Calculate the corresponding value for the y-coordinate, and<br />Repeat.<br />In this way, we can create a table of ordered pairs and plot them on the coordinate plane.<br />Β <br />Make a Table<br />
12. 12. Consider the equation π¦=12π₯+2. <br />Β <br />Make a Table<br />
13. 13. Consider the equation π¦=12π₯+2. <br />Β <br />Make a Table<br />π¦=12(βπ)+2<br />Β <br />=1<br />
14. 14. Consider the equation π¦=12π₯+2. <br />Β <br />Make a Table<br />π¦=12(βπ)+2<br />Β <br />(-2,1)<br />=1<br />
15. 15. Consider the equation π¦=12π₯+2. <br />Β <br />Make a Table<br />π¦=12(βπ)+2<br />Β <br />(-2,1)<br />=1<br />π¦=12(π)+2<br />Β <br />=2<br />(0, 2)<br />
16. 16. Consider the equation π¦=12π₯+2. <br />Β <br />Make a Table<br />π¦=12(βπ)+2<br />Β <br />(-2,1)<br />=1<br />π¦=12(π)+2<br />Β <br />=2<br />(0, 2)<br />π¦=12(π)+2<br />Β <br />(2, 3)<br />=3<br />
17. 17. Another method for graphing lines when an equation is in slope-intercept form is as follows:<br />Use the slope and intercept<br />
18. 18. Another method for graphing lines when an equation is in slope-intercept form is as follows:<br />Plot the y-intercept on the coordinate plane; that's the point (0, b).<br />Use the slope and intercept<br />
19. 19. Another method for graphing lines when an equation is in slope-intercept form is as follows:<br />Plot the y-intercept on the coordinate plane; that's the point (0, b).<br />Use the slope to find another point (and repeat).<br />Use the slope and intercept<br />
20. 20. Another method for graphing lines when an equation is in slope-intercept form is as follows:<br />Plot the y-intercept on the coordinate plane; that's the point (0, b).<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Use the slope and intercept<br />
21. 21. Consider the equationπ¦=β54π₯+7.<br />Β <br />Plot the y-intercept <br />Use the slope and intercept<br />(0, b) = (0, 7)<br />
22. 22. Consider the equationπ¦=β54π₯+7.<br />Β <br />Plot the y-intercept <br />Use the slope to find another point (and repeat).<br />Use the slope and intercept<br />(0, b) = (0, 7)<br />From the intercept, move down 5 and right 4 (or up 5 and left 4).<br />
23. 23. Consider the equationπ¦=β54π₯+7.<br />Β <br />Plot the y-intercept <br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Use the slope and intercept<br />(0, b) = (0, 7)<br />From the intercept, move down 5 and right 4 (or up 5 and left 4).<br />
24. 24. This method is very similar to the slope-intercept method. To graph a line using this method, do the following:<br />Use a point and the slope<br />
25. 25. This method is very similar to the slope-intercept method. To graph a line using this method, do the following:<br />Plot the point (π₯1, π¦1).<br />Β <br />Use a point and the slope<br />
26. 26. This method is very similar to the slope-intercept method. To graph a line using this method, do the following:<br />Plot the point (π₯1, π¦1).<br />Use the slope to find another point (and repeat).<br />Β <br />Use a point and the slope<br />
27. 27. This method is very similar to the slope-intercept method. To graph a line using this method, do the following:<br />Plot the point (π₯1, π¦1).<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Β <br />Use a point and the slope<br />
28. 28. Consider the equationπ¦β2=73(π₯+3).<br />Β <br />Plot the point (π₯1, π¦1)<br />Β <br />Use a point and the slope<br />(π₯1, π¦1)= (-3, 2)<br />Β <br />
29. 29. Consider the equationπ¦β2=73(π₯+3).<br />Β <br />Plot the point (π₯1, π¦1)<br />Use the slope to find another point (and repeat).<br />Β <br />Use a point and the slope<br />(π₯1, π¦1)= (-3, 2)<br />Β <br />From (-3, 2), move up 7 and right 3 -β or down 7 and left 3.<br />
30. 30. Consider the equationπ¦β2=73(π₯+3).<br />Β <br />Plot the point (π₯1, π¦1)<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Β <br />Use a point and the slope<br />(π₯1, π¦1)= (-3, 2)<br />Β <br />From (-3, 2), move up 7 and right 3 -β or down 7 and left 3.<br />
31. 31. This method is used when the line is in Standard Form (π΄π₯+π΅π¦=πΆ). <br />Β <br />Use the Intercepts<br />
32. 32. This method is used when the line is in Standard Form (π΄π₯+π΅π¦=πΆ). <br />The x-intercept is easily calculated by setting y to 0 and solving for π₯.<br />Β <br />Use the Intercepts<br />
33. 33. This method is used when the line is in Standard Form (π΄π₯+π΅π¦=πΆ). <br />The x-intercept is easily calculated by setting y to 0 and solving for π₯.<br />The y-intercept is calculated by setting π₯ to zero and solving for π¦.<br />Β <br />Use the Intercepts<br />
34. 34. This method is used when the line is in Standard Form (π΄π₯+π΅π¦=πΆ). <br />The x-intercept is easily calculated by setting y to 0 and solving for π₯.<br />The y-intercept is calculated by setting π₯ to zero and solving for π¦.<br />Plot the two intercepts and draw a line through them.<br />Β <br />Use the Intercepts<br />
35. 35. Consider the equation3π₯β5π¦=β15.<br />Β <br />Set π¦=0 and solve for π₯.<br />Β <br />Use the Intercepts<br />3π₯=β15; π₯=β5(β5,Β 0)<br />Β <br />
36. 36. Consider the equation3π₯β5π¦=β15.<br />Β <br />Set π¦=0 and solve for π₯.<br />Set π₯=0 and solve for π¦.<br />Β <br />Use the Intercepts<br />3π₯=β15; π₯=β5(β5,Β 0)<br />Β <br />β5π₯=β15; π¦=3(0,Β Β 3)<br />Β <br />
37. 37. Consider the equation3π₯β5π¦=β15.<br />Β <br />Set π¦=0 and solve for π₯.<br />Set π₯=0 and solve for π¦.<br />Draw a line through the points.<br />Β <br />Use the Intercepts<br />3π₯=β15; π₯=β5(β5,Β 0)<br />Β <br />β5π₯=β15; π¦=3(0,Β Β 3)<br />Β <br />