3.1 – Graphing Linear Equations
3.1 – Graphing Linear Equations. Linear equation.
Dec 24, 2015
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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 = Ca. 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 +2x2x + 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 b. 2xy – 5y = 6 +2x +2x2x + 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 b. 2xy – 5y = 6 +2x +2x2x + 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 = Ca. y = 5 – 2x b. 2xy – 5y = 6
+2x +2x
2x + y = 5
c. y = 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 = Ca. y = 5 – 2x b. 2xy – 5y = 6
+2x +2x
2x + y = 5
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 = Ca. y = 5 – 2x b. 2xy – 5y = 6
+2x +2x
2x + y = 5
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
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