finding equations from lines 2

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.

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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?

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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?

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STUDENTS NEEDED TO EXPLAIN

3. 4.

STUDENTS NEEDED TO GRAPH

• 2x + y = 4

• y = −4 EXPLAINATION REQUIRED

• x = 5 EXPLAINATION REQUIRED