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# Solving linear equations alg 2 project anna jen ali

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### Solving linear equations alg 2 project anna jen ali

1. 1. Solving Linear Equations<br />By: Anna Carey, Ali LaBella, and Jen Putnam<br />
2. 2. Linear Equations vs.Linear Functions<br />A linear equationis an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.<br />
3. 3. Examples of Linear Equations<br />Linear EquationsNot Linear Equations<br />7x − 3y = 14 8a + 3b2 = -12 <br />x = 11y=ghghjgfj<br />3s = -2t − 9x + xy= 2<br />y = ¼xy = 1/X<br />
4. 4. Linear Equations cannot…<br /><ul><li>Be raised to a power other than 1
5. 5. Cannot have two variables multiplied by each other</li></ul>Why?<br />
6. 6. Ax + By = C<br /><ul><li>A must be greater than or equal to zero
7. 7. A and B cannot be zero
8. 8. Example: 5x + 7y = 12</li></ul>Standard Form<br />
9. 9. y = mx + b <br /><ul><li>m is the slope of the line
10. 10. b is the y-intercept
11. 11. Example: y = ¾x + 6</li></ul>Slope-Intercept Form<br />
12. 12. y − y1 = m(x − x1)<br /><ul><li>(x1 , y1) are the coordinates of a point on the line
13. 13. m is the slope of the line
14. 14. Example: y +1 =¼(x − 2)</li></ul>Point-Slope Form<br />
15. 15. x/a+y/b = 1<br /><ul><li>a is the x-intercept
16. 16. b is the y-intercept
17. 17. Example: x/2 + y/5 = 1</li></ul>Intercept Form <br />
18. 18. <ul><li>Slope is the ratio of the change in </li></ul> y-coordinates to the change in x-coordinates.<br /> (Rise over Run, Rate of Change)<br />y2− y1= m<br />x2− x1tghr<br />What is slope?<br />
19. 19. <ul><li>The x-intercept is where the line crosses the </li></ul> x-axis.<br /><ul><li>Set y equal to zero
20. 20. Example: 4x + 2y = 8</li></ul> 4x + 2(0) = 8<br /> 4x = 8<br /> x = 2<br /><ul><li>So, the x-intercept is (2, 0)</li></ul>Finding the x-intercept <br />
21. 21. <ul><li>The y-intercept is where the line crosses the </li></ul>y-axis.<br /><ul><li>Set x equal to zero
22. 22. Example: 4x + 2y = 8</li></ul>4(0) + 2y= 8<br />2y = 8<br />y = 4<br /><ul><li>So, the y-intercept is (0, 4)</li></ul>Finding the y-intercept<br />
23. 23. Solve: 3x − 4 = -10<br />Isolate the variable, x<br /><ul><li>3x − 4 (+ 4) = -10 (+ 4)
24. 24. 3x = -6
25. 25. x = -2</li></ul>The solution to this linear equation is x = -2<br />Solving a Linear Equation<br />
26. 26. THE END<br />