finding equations from lines 2
TRANSCRIPT
![Page 1: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/1.jpg)
LINEAR FUNCTIONSAND THEIR GRAPHS
NC GOAL 4.01 Use linear functions or inequalities to model and solve
problems; justify results.Solve using tables, graphs, and
algebraic properties. Interpret constants and coefficients in
the context of the problem.
8-4
![Page 2: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/2.jpg)
8-4
FIND THE EQUATION OF A LINE FROM A GRAPH.
GRAPH A LINEAR FUNCTION USING STANDARD FORM.
![Page 3: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/3.jpg)
• WHAT DO I LOOK FOR ON A GRAPH TO DETERMINE THE SLOPE?
• WHAT IS STANDARD FORM OF A LINEAR FUNCTION?
8-4
![Page 4: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/4.jpg)
8-4
![Page 5: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/5.jpg)
CAN YOU FIND THE EQUATION OF THIS LINE
y = -4x - 2 FIND 2 DISTINCT POINTS ON THE GRAPH TO DETERMINE THE RISE OVER RUN, THEN DETERMINE IF THE SLOPE IS NEGATIVE OR POSITIVE. PUT THAT SLOPE WITH THE y INTERCEPT AND YOU HAVE THE EQUATION!
![Page 6: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/6.jpg)
CAN YOU FIND THE EQUATION OF THIS LINE
y = -1/4x + 3.5Or y = -1/4x + 3 ½
![Page 7: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/7.jpg)
CAN YOU FIND THE EQUATION OF THIS LINE
Y = 1/2x + 3
![Page 8: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/8.jpg)
STANDARD FORM OF A LINEAR FUNCTION
• STANDARD FORM OF A LINEAR FUNCTION IS Ax + By = C AND COULD LOOK LIKE THIS:
2x + 3y = 6 or -x – y = 12
GRAPHING A LINE FROM STANDARD FORM ISALSO AN EASY TASK, BUT ITS GRAPHEDDIFFERENTLY.
![Page 9: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/9.jpg)
UNDERSTANDING IS NECESSARY
• WHEN A LINE CROSSES THE x AXIS, WHAT IS THE y VALUE?
• WHEN A LINE CROSSES THE y AXIS, WHAT IS THE x VALUE?
• LETS LOOK AT THE NEXT SLIDE AND YOU DECIDE.
![Page 10: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/10.jpg)
FIGURING IT OUT
WHAT IS THIS POINT?
(0, 2)WHAT IS THIS POINT?(1,0)
SO WHAT IS y WHEN THE LINE CROSSES THE x AXIS?
WHAT IS x WHEN THE LINE CROSSES THE y AXIS?
![Page 11: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/11.jpg)
SO LETS TRY TO GRAPH A LINE IN STANDARD FORM
• HOW CAN WE GRAPH THIS LINE?• 3x – 4y = 12• LET x = 0 AND SOLVE FOR y• 3(0) – 4y = 12• -4y = 12 -4 -4y = -3 THEREFOR, THIS IS A POINT. (0, -3)
![Page 12: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/12.jpg)
STAY WITH US, THIS IS NOT HARD
• NOW TO FIND THE VALUE OF x• 3x – 4y = 12• LET y = 0 AND SOLVE FOR x• 3x – 4(0) = 12• 3x = 12 3 3x = 4 THEREFOR, THIS IS A POINT. (4, 0)
![Page 13: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/13.jpg)
GRAPHING FROM STANDARD FORM
(0, -3)
(4,0)
AND OUR LINE IS GRAPHED!
3x – 4y = 12
![Page 14: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/14.jpg)
LETS TRY ANOTHER ONE
• 2x + y = 4LET x = 0 AND YOU HAVE y = 4
LET y = 0 AND Y0U HAVE 2x = 4 SO x = 2
THE ORDERED PAIRS ARE (0,4) AND (2,0)
SEE NEXT SLIDE
![Page 15: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/15.jpg)
THE GRAPH
2x + y = 4
![Page 16: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/16.jpg)
NOW YOU TRY
x + 6y = 6 DID YOU GET IT?
![Page 17: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/17.jpg)
WHAT IS THIS
THIS LINE HAS A y INTERCEPT OF 4, BUT WHAT IS UP WITH THE SLOPE?
NO SLOPE HAPPENING HERE!
THE EQUATION MUST THEN BE y = 0x + 4OR BETTER WRITTEN AS y = 4
![Page 18: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/18.jpg)
WHAT IS THIS
SO, WHAT IS THIS ONE?
THIS CROSSES THE x AXIS AT -5, hmmmm, WHATS UP WITH THIS SLOPE?
THIS SLOPE IS UNDEFINED, SO THIS EQUATION IS X = -5
![Page 19: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/19.jpg)
THE BIG PICTURE
UNDEFINED
X =
NO SLOPE, y =
![Page 20: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/20.jpg)
WORKTIME
• GRAPH THESE LINES ON THE GRAPH PAPER PROVIDED.
1.x + y = −42.2x + y = 43.2x + 3y = 64.5x − 2y = 105.x = 56. y = −4
![Page 21: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/21.jpg)
FIND THE EQUATION OF THESE LINES
1. 2.
![Page 22: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/22.jpg)
3. 4.
![Page 23: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/23.jpg)
CONTINUE WITH SLIDES FOR CLOSING
![Page 24: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/24.jpg)
8-4
FIND THE EQUATION OF A LINE FROM A GRAPH.
GRAPH A LINEAR FUNCTION USING STANDARD FORM.
![Page 25: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/25.jpg)
• WHAT DO I LOOK FOR ON A GRAPH TO DETERMINE THE SLOPE?
• WHAT IS STANDARD FORM OF A LINEAR FUNCTION?
8-4
![Page 26: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/26.jpg)
STUDENTS NEEDED TO EXPLAIN
3. 4.
![Page 27: Finding equations from lines 2](https://reader034.vdocuments.us/reader034/viewer/2022052706/58ef489e1a28ab69128b458b/html5/thumbnails/27.jpg)
STUDENTS NEEDED TO GRAPH
• 2x + y = 4
• y = −4 EXPLAINATION REQUIRED
• x = 5 EXPLAINATION REQUIRED