2.2 – linear equations
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2.2 – Linear Equations. 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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/1.jpg)
2.2 – Linear Equations
![Page 2: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/2.jpg)
2.2 – Linear EquationsLinear equation
![Page 3: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/3.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
![Page 4: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/4.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction,
![Page 5: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/5.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication,
![Page 6: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/6.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
![Page 7: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/7.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
![Page 8: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/8.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
![Page 9: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/9.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
Linear Eqs.
![Page 10: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/10.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
Linear Eqs.
5x – 3y = 7
![Page 11: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/11.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a
variable by a number.
Linear Eqs.
5x – 3y = 7
x = 9
![Page 12: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/12.jpg)
2.2 – Linear EquationsLinear 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
![Page 13: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/13.jpg)
2.2 – Linear EquationsLinear 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
![Page 14: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/14.jpg)
2.2 – Linear EquationsLinear 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
![Page 15: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/15.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 6s = -3t – 15 y = ½x
![Page 16: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/16.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 6s = -3t – 15 y = ½x
![Page 17: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/17.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 y = ½x
![Page 18: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/18.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 y = ½x
![Page 19: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/19.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 x + xy = 1y = ½x
![Page 20: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/20.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by a number.
Linear Eqs. Non-linear Eqs.5x – 3y = 77a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 x + xy = 1y = ½x
![Page 21: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/21.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by
a number.Linear Eqs. Non-linear Eqs.5x – 3y = 7 7a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 x + xy = 1y = ½x y = 1
x
![Page 22: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/22.jpg)
2.2 – Linear EquationsLinear equation – equation with only addition,
subtraction, multiplication, and division of a variable by
a number.Linear Eqs. Non-linear Eqs.5x – 3y = 7 7a + 4b2 = -8x = 9 y = √x + 56s = -3t – 15 x + xy = 1y = ½x y = 1
x
![Page 23: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/23.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
![Page 24: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/24.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x
![Page 25: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/25.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
![Page 26: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/26.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5
![Page 27: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/27.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5 NO
![Page 28: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/28.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5 NO; exponent on var.
![Page 29: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/29.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5 NO; exponent on var.
(c) h(x,y) = 2xy
![Page 30: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/30.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5 NO; exponent on var.
(c) h(x,y) = 2xy NO
![Page 31: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/31.jpg)
Example 1 State whether each function or equation is linear. If no, explain why.
(a) f(x) = 10 – x YES
(b) g(x) = x4 – 5 NO; exponent on var.
(c) h(x,y) = 2xy NO; multiplying vars.
![Page 32: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/32.jpg)
• Standard Form
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• Standard Form = Ax + By = C
![Page 34: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/34.jpg)
• Standard Form = Ax + By = C
*Get x’s and y’s on left side,
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• Standard Form = Ax + By = C
*Get x’s and y’s on left side, numbers on rt.
![Page 36: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/36.jpg)
• 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.
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• 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
![Page 38: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/38.jpg)
• 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
+2x +2x
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• 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
+2x +2x
2x + y = 3
![Page 40: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/40.jpg)
• 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
+2x +2x
2x + y = 3
A=2
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• 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
+2x +2x
2x + y = 3
A=2,B=1
![Page 42: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/42.jpg)
• 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
+2x +2x
2x + y = 3
A=2,B=1 ,&C=3
![Page 43: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/43.jpg)
• 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 + 2
+2x +2x
2x + y = 3
A=2,B=1,&C=3
![Page 44: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/44.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 A=2,B=1,&C=3
![Page 45: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/45.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2
A=2,B=1,&C=3
![Page 46: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/46.jpg)
• 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 + 2
+2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2
A=2,B=1,&C=3 8(⅜x – 3y) = (2)8
![Page 47: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/47.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2A=2,B=1,&C=3 8(⅜x – 3y) = (2)8
3x – 24y = 16
![Page 48: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/48.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2A=2,B=1,&C=3 8(⅜x – 3y) = (2)8
3x – 24y = 16A=3
![Page 49: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/49.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2A=2,B=1,&C=3 8(⅜x – 3y) = (2)8
3x – 24y = 16A=3,B=-24
![Page 50: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/50.jpg)
• 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 + 2 +2x +2x -3y -3y
2x + y = 3 ⅜x – 3y = 2A=2,B=1,&C=3 8(⅜x – 3y) = (2)8
3x – 24y = 16A=3,B=-
24,&C=16
![Page 51: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/51.jpg)
• x-intercept
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• x-intercept – (x, 0)
![Page 53: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/53.jpg)
• x-intercept – (x, 0); y-intercept
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• x-intercept – (x, 0); y-intercept – (0, y)
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• 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.
![Page 56: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/56.jpg)
• 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
![Page 57: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/57.jpg)
• 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
+ 12 +12
![Page 58: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/58.jpg)
• 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
+ 12 +12
3x – 4y = 12
![Page 59: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/59.jpg)
• 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
+ 12 +12
3x – 4y = 12
x-int.
![Page 60: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/60.jpg)
• 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
+ 12 +12
3x – 4y = 12
x-int. 3x – 4(0) = 12
![Page 61: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/61.jpg)
• 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
+ 12 +12
3x – 4y = 12
x-int. 3x – 4(0) = 12
(y=0) 3x = 12
![Page 62: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/62.jpg)
• 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
+ 12 +12
3x – 4y = 12
x-int. 3x – 4(0) = 12
(y=0) 3x = 12
3 3
![Page 63: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/63.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 (y=0) 3x = 12
3 3 x = 4
![Page 64: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/64.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 (y=0) 3x = 12
3 3 x = 4 (4, 0)
![Page 65: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/65.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 (y=0) 3x = 12
3 3 x = 4 (4, 0)
![Page 66: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/66.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. (y=0) 3x = 12
3 3 x = 4 (4, 0)
![Page 67: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/67.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12
3 3 x = 4 (4, 0)
![Page 68: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/68.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12 (x=0) -4y = 12
3 3 x = 4 (4, 0)
![Page 69: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/69.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12 (x=0) -4y = 12
3 3 -4 -4 x = 4 (4, 0)
![Page 70: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/70.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12 (x=0) -4y = 12
3 3 -4 -4 x = 4 y = -3 (4, 0)
![Page 71: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/71.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12 (x=0) -4y = 12
3 3 -4 -4 x = 4 y = -3 (4, 0) (0, -
3)
![Page 72: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/72.jpg)
• 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
+ 12 +12 3x – 4y = 12
x-int. 3x – 4(0) = 12 yint. 3(0) – 4y = 12(y=0) 3x = 12 (x=0) -4y = 12
3 3 -4 -4 x = 4 y = -3 (4, 0) (0, -
3)
![Page 73: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/73.jpg)
(4,0) (0,-3)x-int. = y-int. =
![Page 74: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/74.jpg)
(4,0) (0,-3)x-int. = y-int. =
![Page 75: 2.2 – Linear Equations](https://reader036.vdocuments.site/reader036/viewer/2022062520/5681574f550346895dc4f211/html5/thumbnails/75.jpg)
(4,0) (0,-3)x-int. = y-int. =