Solving linear equations alg 2 project anna jen ali
- 1. Solving Linear EquationsBy: Anna Carey, Ali LaBella, and Jen Putnam
- 2. Linear Equations vs.Linear FunctionsA linear equationis an equation that has no operations other than addition, subtraction, and multiplication of a variable by a constant.
- 3. Examples of Linear EquationsLinear EquationsNot Linear Equations7x − 3y = 14 8a + 3b2 = -12 x = 11y=ghghjgfj3s = -2t − 9x + xy= 2y = ¼xy = 1/X
- 4. Linear Equations cannot…Be raised to a power other than 1
- 5. Cannot have two variables multiplied by each otherWhy?
- 6. Ax + By = CA must be greater than or equal to zero
- 7. A and B cannot be zero
- 8. Example: 5x + 7y = 12Standard Form
- 9. y = mx + b m is the slope of the line
- 10. b is the y-intercept
- 11. Example: y = ¾x + 6Slope-Intercept Form
- 12. y − y1 = m(x − x1)(x1 , y1) are the coordinates of a point on the line
- 13. m is the slope of the line
- 14. Example: y +1 =¼(x − 2)Point-Slope Form
- 15. x/a+y/b = 1a is the x-intercept
- 16. b is the y-intercept
- 17. Example: x/2 + y/5 = 1Intercept Form
- 18. Slope is the ratio of the change in y-coordinates to the change in x-coordinates. (Rise over Run, Rate of Change)y2− y1= mx2− x1tghrWhat is slope?
- 19. The x-intercept is where the line crosses the x-axis.Set y equal to zero
- 20. Example: 4x + 2y = 8 4x + 2(0) = 8 4x = 8 x = 2So, the x-intercept is (2, 0)Finding the x-intercept
- 21. The y-intercept is where the line crosses the y-axis.Set x equal to zero
- 22. Example: 4x + 2y = 84(0) + 2y= 82y = 8y = 4So, the y-intercept is (0, 4)Finding the y-intercept
- 23. Solve: 3x − 4 = -10Isolate the variable, x3x − 4 (+ 4) = -10 (+ 4)
- 24. 3x = -6
- 25. x = -2The solution to this linear equation is x = -2Solving a Linear Equation
- 26. THE END