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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
8-4
FIND THE EQUATION OF A LINE FROM A GRAPH.
GRAPH A LINEAR FUNCTION USING STANDARD FORM.
• WHAT DO I LOOK FOR ON A GRAPH TO DETERMINE THE SLOPE?
• WHAT IS STANDARD FORM OF A LINEAR FUNCTION?
8-4
8-4
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!
CAN YOU FIND THE EQUATION OF THIS LINE
y = -1/4x + 3.5Or y = -1/4x + 3 ½
CAN YOU FIND THE EQUATION OF THIS LINE
Y = 1/2x + 3
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.
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.
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?
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)
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)
GRAPHING FROM STANDARD FORM
(0, -3)
(4,0)
AND OUR LINE IS GRAPHED!
3x – 4y = 12
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
THE GRAPH
2x + y = 4
NOW YOU TRY
x + 6y = 6 DID YOU GET IT?
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
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
THE BIG PICTURE
UNDEFINED
X =
NO SLOPE, y =
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
FIND THE EQUATION OF THESE LINES
1. 2.
3. 4.
CONTINUE WITH SLIDES FOR CLOSING
8-4
FIND THE EQUATION OF A LINE FROM A GRAPH.
GRAPH A LINEAR FUNCTION USING STANDARD FORM.
• WHAT DO I LOOK FOR ON A GRAPH TO DETERMINE THE SLOPE?
• WHAT IS STANDARD FORM OF A LINEAR FUNCTION?
8-4
STUDENTS NEEDED TO EXPLAIN
3. 4.
STUDENTS NEEDED TO GRAPH
• 2x + y = 4
• y = −4 EXPLAINATION REQUIRED
• x = 5 EXPLAINATION REQUIRED