Transcript 4.5 – Graphing Linear Equations

3.1 – Graphing Linear Equations
3.1– Graphing Linear Equations
•
Linear equation
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
b. 2xy – 5y = 6
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight
line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation
is a linear equation. If so, write the
equation in standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
b. 2xy – 5y = 6
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation is a
linear equation. If so, write the equation in
standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
c. y = 9
b. 2xy – 5y = 6
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation is a
linear equation. If so, write the equation in
standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
b. 2xy – 5y = 6
c. y = 9
d. y = 4x2 – 9
3.1– Graphing Linear Equations
•
Linear equation – its graph is a straight line
 IDENTIFYING LINEAR EQUATIONS
Ex.1 Determine whether each equation is a
linear equation. If so, write the equation in
standard form.
*Standard Form: Ax + By = C
a. y = 5 – 2x
+2x
+2x
2x + y = 5
b. 2xy – 5y = 6
c. y = 9
d. y = 4x2 – 9
GRAPHING LINEAR EQUATIONS
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
GRAPHING LINEAR EQUATIONS
Ex. 2 Graph the following equations.
a. y = 2x – 3
x
2x – 3
y
(x, y)
-1 2(-1) – 3 -5 (-1, -5)
0
2(0) – 3 -3
(0, -3)
1
2(1) – 3 -1
(1, -1)
b.
x + 2y = 6
b. x + 2y = 6
*Find x and y-intercepts!
b. x + 2y = 6
*Find x and y-intercepts!
x-int:
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x+ 0 =6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int:
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
b. x + 2y = 6
*Find x and y-intercepts!
x-int: x + 2(0) = 6
x=6
(6,0)
y-int: (0) + 2y = 6
2y = 6
2 2
y=3
(0,3)
GRAPHS AS FUNCTIONS
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
a.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
*Vertical Line Test – If you can draw vertical
line anywhere on graph & it
crosses more than once,
then it’s not a function!
a.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
*Vertical Line Test – If you can draw vertical
line anywhere on graph & it
crosses more than once,
then it’s not a function!
a.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
*Vertical Line Test – If you can draw vertical
line anywhere on graph & it
crosses more than once,
then it’s not a function!
a.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
*Vertical Line Test – If you can draw vertical
line anywhere on graph & it
crosses more than once,
then it’s not a function!
a.
GRAPHS AS FUNCTIONS
Ex. 3 Determine whether or not each graph is
a function.
*Vertical Line Test – If you can draw vertical
line anywhere on graph & it
crosses more than once,
then it’s not a function!
a.
FUNCTION
b.
b.
FUNCTION
b.
FUNCTION
c.
b.
FUNCTION
c.
NOT A
FUNCTION