pres graphing linear equations (section 1.1)
TRANSCRIPT
![Page 1: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/1.jpg)
Chapter 1.1
![Page 2: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/2.jpg)
Is that equation linear?
• y = 3x – 4
![Page 3: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/3.jpg)
Is that equation linear?
• y = 3x – 4
The equation is in the form y = mx + b,
where m = 3 and b = -4, so the equation
IS LINEAR.
![Page 4: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/4.jpg)
Is that equation linear?
• 3y = x + 9
![Page 5: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/5.jpg)
Is that equation linear?
• 3y = x + 9
Can the equation be arranged into theform y = mx + b?
![Page 6: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/6.jpg)
Is that equation linear?
• 3y = x + 9
Can the equation be arranged into theform y = mx + b?
Yes
![Page 7: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/7.jpg)
Is that equation linear?
• 3y = x + 9 Divide both sides by 3.y = 1/3 x + 3
The equation is in the form y = mx + b,where m = 1/3 and b = 3, so the
equationIS LINEAR.
![Page 8: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/8.jpg)
Is that equation linear?
• 4y + 16 = 2x
![Page 9: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/9.jpg)
Is that equation linear?
• 4y + 16 = 2x
Can the equation be arranged into theform y = mx + b?
![Page 10: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/10.jpg)
Is that equation linear?
• 4y + 16 = 2x
Can the equation be arranged into theform y = mx + b?
Yes
![Page 11: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/11.jpg)
Is that equation linear?
• 4y + 16 = 2x Subtract 16 from both sides of the equation.
4y = 2x – 16 Divide both sides of the equation by 4.
y = ½x – 4
The equation is in the form y = mx + b,where m = ½ and b = -4, so the equationIS LINEAR.
![Page 12: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/12.jpg)
Graph: y = -2x + 3
![Page 13: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/13.jpg)
Graph: y = -2x + 3
• m = -2/1• y-intercept = 3
• Start the graph at y-int (3).
• Use the slope (-2/1) and go down 2 and over 1.
![Page 14: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/14.jpg)
Graph: y = 4x - 2
![Page 15: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/15.jpg)
Graph: y = 4x - 2
• m = 4/1• y-intercept = -2
• Start the graph at y-int (-2).
• Use the slope (4/1) and go up 4 and over 1.
![Page 16: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/16.jpg)
Graph: 6y + 36 = 6x
![Page 17: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/17.jpg)
Graph: 6y + 36 = 6x
• Rearrange into y=mx+b.• Subtract 36 from both
sides 6y = 6x – 36.• Divide both sides by
6 y = x + 6.• m = 1/1• y-intercept = 6
• Start the graph at y-int (6).
• Use the slope (1/1) and go up 1 and over 1.
![Page 18: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/18.jpg)
Does that table represent a linear equation? If so, provide
an additional ordered pair.
X Y
2 1
4 2
6 3
8 4
• Do the values of x increase at the same rate? Yes, they all increase by 2.
• Do the values of y increase at the same rate? Yes, they all increase by 1.
• If you answered “yes” to both of these questions, then the table represents a linear equation.
![Page 19: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/19.jpg)
Does that table represent a linear equation? If so, provide
an additional ordered pair.
X Y
2 1
4 2
6 3
8 4
• Do the values of x increase at the same rate?
• Do the values of y increase at the same rate?
• If you answered “yes” to both of these questions, then the table represents a linear equation.
![Page 20: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/20.jpg)
Does that table represent a linear equation? If so, provide
an additional ordered pair.
X Y
3 -1
6 -3
9 -5
11 -7
• Do the values of x increase at the same rate?
• Do the values of y increase at the same rate?
![Page 21: Pres Graphing Linear Equations (Section 1.1)](https://reader036.vdocument.in/reader036/viewer/2022062708/55895da6d8b42a543f8b46d2/html5/thumbnails/21.jpg)
Does that table represent a linear equation? If so, provide
an additional ordered pair.
X Y
3 -1
6 -3
9 -5
11 -7
• Do the values of x increase at the same rate? No
• Do the values of y increase at the same rate? Yes, they all decrease by 2.
• We answered “No” to the first question, so it does not represent a linear equation.