#### 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