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
8-4
FIND THE EQUATION OF A LINE FROM A
GRAPH.
GRAPH A LINEAR FUNCTION USING
STANDARD FORM.
8-4
• 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 + 3.5
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
SO WHAT IS y
WHEN THE
LINE CROSSES
THE x AXIS?
WHAT IS x WHEN
THE LINE
CROSSES THE y
AXIS?
WHAT IS THIS
POINT?
(0, 2)
WHAT IS THIS
POINT?
(1,0)
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 -4
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 = 12
3 3
x = 4 THEREFOR, THIS IS A POINT. (4, 0)
GRAPHING FROM STANDARD FORM
3x – 4y = 12
(4,0)
AND OUR
LINE IS
GRAPHED!
(0, -3)
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
NO SLOPE HAPPENING HERE!
THIS LINE HAS A y INTERCEPT OF 4,
BUT WHAT IS UP WITH THE SLOPE?
THE EQUATION MUST THEN
BE y = 0x + 4
OR BETTER WRITTEN AS y = 4
WHAT IS THIS
SO, WHAT IS THIS ONE?
THIS SLOPE
IS
UNDEFINED,
SO THIS
EQUATION IS
X = -5
THIS CROSSES THE x AXIS AT -5,
hmmmm, WHATS UP WITH THIS
SLOPE?
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.
8-4
• WHAT DO I LOOK FOR ON A GRAPH TO
DETERMINE THE SLOPE?
• WHAT IS STANDARD FORM OF A LINEAR
FUNCTION?
STUDENTS NEEDED TO EXPLAIN
3.
4.
STUDENTS NEEDED TO GRAPH
• 2x + y = 4
• y = −4 EXPLAINATION REQUIRED
• x = 5 EXPLAINATION REQUIRED