2.4 Writing Linear Equations

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