2.2 – Linear Equations. Linear equation 2.2 – Linear Equations Linear equation – equation with only addition,

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2.2 – Linear Equations

Linear equation

2.2 – Linear Equations Linear equation – equation with only addition,

2.2 – Linear Equations Linear equation – equation with only addition, subtraction,

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication,

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number.

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 7 x = 9 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x y = 1 x

2.2 – Linear Equations Linear equation – equation with only addition, subtraction, multiplication, and division of a variable by a number. Linear Eqs.Non-linear Eqs. 5x – 3y = 77a + 4b 2 = -8 x = 9y = √x + 5 6s = -3t – 15x + xy = 1 y = ½x y = 1 x

Example 1State whether each function or equation is linear. If no, explain why.

(a) f(x) = 10 – x

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var.

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xy

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xyNO

Example 1State whether each function or equation is linear. If no, explain why. (a) f(x) = 10 – x YES (b) g(x) = x 4 – 5NO; exponent on var. (c) h(x,y) = 2xyNO; multiplying vars.

Standard Form

Standard Form = Ax + By = C

*Get x’s and y’s on left side,

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt.

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C.

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x x +2x

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x x +2x 2x + y = 3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x x +2x 2x + y = 3 A=2

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x x +2x 2x + y = 3 A=2,B=1

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x x +2x 2x + y = 3 A=2,B=1,&C=3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x 2x + y = 3 A=2,B=1,&C=3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 A=2,B=1,&C=3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3,B=-24

Standard Form = Ax + By = C *Get x’s and y’s on left side, numbers on rt. Example 2 Write each equation in standard form. Identify A, B, and C. (a) y = -2x + 3(b) ⅜x = 3y x +2x -3y -3y 2x + y = 3 ⅜x – 3y = 2 A=2,B=1,&C=3 8(⅜x – 3y) = (2)8 3x – 24y = 16 A=3,B=-24,&C=16

x-intercept

x-intercept – (x, 0)

x-intercept – (x, 0); y-intercept

x-intercept – (x, 0); y-intercept – (0, y)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation.

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = 0

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 =

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int.

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x =

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. (y=0) 3x = 12 3 x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12 3 x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = 12 3 x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = x = 4 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = x = 4y = -3 (4, 0)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = x = 4y = -3 (4, 0)(0, -3)

x-intercept – (x, 0); y-intercept – (0, y) Example 3 Find the x and y intercepts of 3x – 4y – 12 = 0. Then graph the equation. 3x – 4y – 12 = x – 4y = 12 x-int. 3x – 4(0) = 12yint. 3(0) – 4y = 12 (y=0) 3x = 12(x=0) -4y = x = 4y = -3 (4, 0)(0, -3)

(4,0)(0,-3)x-int. =y-int. =

(4,0)(0,-3)x-int. =y-int. =

(4,0)(0,-3)x-int. =y-int. =