LINEAR FUNCTIONS AND 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

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

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 Or 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 IS ALSO AN EASY TASK, BUT ITS GRAPHED DIFFERENTLY.

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 = y = -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 = x = 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 = 4 LET 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 + 4 OR 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 = −4 2.2x + y = 4 3.2x + 3y = 6 4.5x − 2y = 10 5.x = 5 6. 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