3.1 – Graphing Linear Equations

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Presentation transcript:

3.1 – Graphing Linear Equations

3.1– Graphing Linear Equations

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 = 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 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) 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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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) 2(0) – 3 -3 (0, -3) 1 2(1) – 3 (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