1 / 23

2.4 Writing Linear Equations

2.4 Writing Linear Equations. Using point-slope form. Slope-intercept form of a linear equations. y = mx +b Remember m is slope and b is the y intercept If we are given points, then we will have to find the slope. Write the equation in Slope-Intercept form.

dane-gordon
Télécharger la présentation

2.4 Writing Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 2.4 Writing Linear Equations Using point-slope form

  2. Slope-intercept form of a linear equations y = mx +b Remember m is slope and b is the y intercept If we are given points, then we will have to find the slope.

  3. Write the equation in Slope-Intercept form The line has a slope of -3/5 and passes through (5, -2).

  4. Write the equation in Slope-Intercept form The line has a slope of -3/5 and passes through (5, -2). So x = 5 and y = -2 also m = -3/5. - 2 = -3/5(5) + b Must find b

  5. Write the equation in Slope-Intercept form The line has a slope of -3/5 and passes through (5, -2). So x = 5 and y = -2 also m = -3/5. - 2 = -3/5(5) + b Must find b - 2 = -3 + b Add 3

  6. Write the equation in Slope-Intercept form The line has a slope of -3/5 and passes through (5, -2). So x = 5 and y = -2 also m = -3/5. - 2 = -3/5(5) + b Must find b - 2 = -3 + b Add 3 1 = b

  7. Write the equation in Slope-Intercept form The line has a slope of -3/5 and passes through (5, -2). So x = 5 and y = -2 also m = -3/5. 1 = b So the equation is written as y = -3/5 x + 1

  8. Write the equation in Slope-Intercept form Given the points (2, - 3) and (- 3, 7). What do you need first?

  9. Write the equation in Slope-Intercept form Given the points (2, - 3) and (- 3, 7). What do you need first? Slope: the formula is

  10. Write the equation in Slope-Intercept form Given the points (2, - 3) and (- 3, 7). m = ( - 3) – (7) = -10 = -2 ( 2 ) – ( - 3) 5 Now we can use either point to find “b” Lets use ( -3, 7) 7 = - 2( - 3) + b 7 = 6 + b 1 = b With m and b y = - 2x + 1

  11. Point slope form Here we do not have to solve for b Given a point and a slope, we can write an equation. Lets use the points from the last problem (2, - 3) and (- 3, 7). The slope of the line was -2.

  12. Point slope form Given a point and a slope, we can write an equation. (2, - 3) and (- 3, 7) and slope of the line -2. Point-slope Formula y – y1 = m(x – x1) Filling in using a point and slope we have the equation y – 7 = -2(x – (-3)) or y – (- 3) = - 2(x – 2)

  13. Point slope form Which one is right, lets solve for y in both y – 7 = -2(x – (-3)) or y – (- 3) = - 2(x – 2) y – 7 = -2x – 6 y + 3 = -2x + 4 y = - 2x + 1 y = - 2x + 1 Since the equations are the same it does not matter which point we use.

  14. Using point-slope with parallel or perpendicular lines Write an equation parallel to the line y = 3x – 4 and passes through the point (2, - 4). The slope is 3; y – ( - 4) = 3(x – 2)

  15. Using point-slope with parallel or perpendicular lines Write an equation parallel to the line y = 3x – 4 and passes through the point (2, - 4). The slope is 3; y – ( - 4) = 3(x – 2) y + 4 = 3x - 6

  16. Using point-slope with parallel or perpendicular lines Write an equation parallel to the line y = 3x – 4 and passes through the point (2, - 4). The slope is 3; y – ( - 4) = 3(x – 2) y + 4 = 3x – 6 y = 3x - 10

  17. Using linear equation in a word problem. As a part-time salesperson, Jean Stock is paid a daily salary plus commission. When her sales are $100, she makes $58. When her sales are $300, she makes $78. Write the linear equation to model this situation.

  18. Using linear equation in a word problem. her sales are $100, she makes $58 (100,58). When her sales are $300, she makes $78 (300, 78). Find slope 78 – 58 = 20 = 0.1 300 – 100 200 What is her daily Salary? (if she sales nothing)

  19. Using linear equation in a word problem. What is her daily Salary? (if she sales nothing) What is her commission rate? If she sales $100, she makes $58 The slope of the line is 0.1 y – 58 = 0.1(x – 100) y – 58 = 0.1x - 10 y = 0.1x + 48

  20. y = 0.1x + 48 So she earns $48 for just being there. Commission rate is 0.1 or 10% What would she earn if she sold $500?

  21. y = 0.1x + 48 So she earns $48 for just being there. Commission rate is 0.1 or 10% What would she earn if she sold $500? y =0.1(500) + 48 y = 50 + 48 y = $98

  22. Homework Page 78 – 80 #13 – 17 odd,21, 22 23 – 37 odd, 49, 50

  23. Homework Page 78 – 80 #14 – 18 even 24 – 38 odd, 41 - 43

More Related