3.1 – Graphing Linear Equations. Linear equation.

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Presentation transcript:

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 b. 2xy – 5y = 6 +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 b. 2xy – 5y = 6 +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 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 = C a. y = 5 – 2x b. 2xy – 5y = 6 +2x +2x 2x + y = 5 c. y = 9 d. y = 4x 2 – 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 b. 2xy – 5y = 6 +2x +2x 2x + y = 5 c. y = 9 d. y = 4x 2 – 9

 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 x2x – 3y(x, y)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

 GRAPHING LINEAR EQUATIONS Ex. 2 Graph the following equations. a. y = 2x – 3 x2x – 3y(x, y) 2(-1) – 3-5(-1, -5) 02(0) – 3-3(0, -3) 12(1) – 3(1, -1)

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 = 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 = 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 = 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 = 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 = 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 = 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 = 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 = y = 3 (0,3)

 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