1. Monday, 1/12 Warm-up It snowed 6 inches already and it is expected to snow another 2 inches every hour. 1.Write an equation representing the total snowfall y and time x. y = 2x + 6 2. Identify the slope and y-intercept in the equation. Slope = 2 y-intercept = 6

2. Writing the Equation of a line Algebra 1 Unit 5

3. This week we will be: Writing an Equation of a Line Given… 1. Slope and y-intercept 2. Slope and one point 3. Two points 4. Graph

4. First, let’s do a little Review of Slope-Intercept Form The slope-intercept form of a linear equation is… y = mx + b slope y-intercept

5. Review of Slope-Intercept Form – Quick Practice y = –4x + 3 m = –4, b = 3 y = ½x – 5 m = ½, b = –5 Identify the slope and y-intercept of each equation:

6. 1. Write the Equation of the Line Given the Slope and y-intercept 1. Use the slope-intercept form: y = mx + b 2. Substitute the slope for m and y-intercept for b Example 1: m = 3, b = 1 y = mx + b y = 3x + 1 Example 2: m = –2, b = –4 y = mx + b y = –2x + – 4 OR y = –2x – 4

7. 1.Write the Equation of the Line Given the Slope and y-intercept Now YOU try… 1. m = 5, b = 2 2. m = 1/2, b = –3 3. m = –4, b = 0 y = 5x + 2 y = ½x – 3 y = –4x + 0 OR y = –4x GOOD JOB!

8. 2. Write the Equation of the Line Given the Slope and One Point 1. Use the slope-intercept form: y = mx + b 2. Substitute the slope for m and the point for y and x 3. Solve for b 4. Use slope-intercept form again. Substitute slope for m and the y-intercept for b Example 1: Given m = 3 and (2, 4) 4 = (3) (2) + b simplify 3*2 4 = 6 + b -6 -6 subtract 6 from both sides --------------- -2 = b y = 3x + -2 or y = 3x – 2

9. 2. Write the Equation of the Line Given the Slope and One Point 1. Use the slope-intercept form: y = mx + b 2. Substitute the slope for m and the point for y and x 3. Solve for b 4. Use slope-intercept form again. Substitute slope for m and the y-intercept for b Example 2: Given m = -2 and (1, 5) 5 = (-2) (1) + b simplify -2*1 5 = -2 + b +2 +2 add 2 to both sides --------------- 7 = b y = -2x + 7

10. 2. Write the Equation of the Line Given the Slope and One Point Now YOU try… 1. m = 5, (4,2) 2. m = -3, (2, 1) 3. m = 6, (3, 5) 4. m = -1, (5,0) y = 5x – 18 y = -3x + 7 y = 6x – 13 y = -1x + 5

11. 2. Write the Equation of the Line Given the Slope and One Point HOMEWORK: p. 331 (#1-6) Write equation in slope-intercept form for each line with the given point and slope. 1. (2, 5), m = 5 4. (1, 2), m = -1 2. (-3, 0), m = -2 5. (2, -6), m = 1 3. (2, 4), m = 3 6. (-3, 0), m = -3 *change in #3 and #4

12. Tuesday, 1/13 Warm-up Find the slope of the line that contains the two points (4, 2) and (1, 8) m = --------- m = --------- = -2 y 2 – y 1 x 2 – x 1 8 – 2 1 – 4 6 -3

13. 3. Write the Equation of the Line Given Two Points To write an equation in slope-intercept form, y = mx + b, we must know the SLOPE and Y-INTERCEPT When given just two points (x 1, y 1 ) and (x 2, y 2 )… we do not know the slope or the y-intercept! SO.. We need to find both the slope and y-intercept It’s easy! You already know how!

14. 3. Write the Equation of the Line Given Two Point Example 1: (2, 3) and (4, 7) x 1, y 1 x 2, y 2 1. Find the slope: m = ----------- m = ------- = ---- = 2 2. Using slope-intercept form 3. Substitute slope for m and EITHER POINT for x and y 3 = 2(2) + b y = mx + b 4. Solve for b 3 = 2(2) + b simplify 2*2 3 = 4 + b -4 -4 subtract 4 from --------------- both sides -1 = b 5. Use slope-intercept form again. Substitute slope for m and y-intercept for b y = 2x – 1 x 2 – x 1 y 2 – y 1 7 – 3 4 – 2 4 2

15. 3. Write the Equation of the Line Given Two Points Example 2: (3, 2) and (5, -4) x 1, y 1 x 2, y 2 1. Find the slope: m = ----------- m = -------- = ---- = -3 2. Using slope-intercept form 3. Substitute slope for m and EITHER POINT for x and y 2 = -3(3) + b 4. Solve for b 2 = -3(3) + b simplify -3*3 2 = -9 + b +9 +9 add 9 from both -------------- sides 11 = b 5. Use slope-intercept form again. Substitute slope for m and y-intercept for b y = -3x + 11 y 2 – y 1 x 2 – x 1 -4 – 2 5 – 3 -6 2

16. 3. Write the Equation of the Line Given Two Points Now YOU try… 1. (2, 3) (4, 7) m = 2 b = -1 2. (-2, 3) (1, -6) m = -3 b = -3 3. (0, -3) (-2, 5) m = -4 b = -3 y = 2x – 1 y = -3x – 3 y = -4x – 3

17. 3. Write the Equation of the Line Given Two Points HOMEWORK: p. 331 (#13-18) Write an equation for each line that contains the given points. 13. (-6,1) (2,3) 16. (0,0) (4,2) 14. (12, 16) (1,5) 17. (3,2) (1,5) 15. (0,4), (4,2) 18. (-4,1) (-1,4) *Some answers will be fractions – be careful when adding/subtracting or multiplying two fractions

18. Wednesday, 1/14 Warm-up Identify the y-intercept and find the slope (rise/run) in the graph below. b = -3 m = 3/2 3 2

19. 1. Write the Equation of the Line Given a Graph Case 1: 1. Identify y-intercept 2. Find slope (rise/run) 3. Substitute slope for m and y-intercept for b in slope- intercept form. y = 3/2x – 3 Example from Warm-up 3 2 b = -3 m = 3/2

20. 1. Write the Equation of the Line Given a Graph Case 2: 1. Identify two points 2. Find slope: m = ---------- 3. Substitute slope for m and either point for x and y. 4. Solve for b. 5. Substitute slope for m and y-intercept for b in slope- intercept form. Example: y 2 – y 1 x 2 – x 1 (-1, - 3) (1, 3)

21. 1. Write the Equation of the Line Given a Graph Case 2: 1. Identify two points 2. Find slope: m = ---------- 3. Substitute slope for m and either point for x and y. 4. Solve for b. 5. Substitute slope for m and y-intercept for b in slope- intercept form. 1. (-1, -3) (1, 3) 2. m = ---------- = ------ = 3. 3 = 3(1) + b 3 = 3 + b simplify 3*1 -3 -3 subtract 3 from both sides ------------------------- 0 = b 5. y = 3x + 0 or y = 3x y 2 – y 1 x 2 – x 1 3 – (-3) 1 – (-1) 6 2 3

22. Exploring the Graph and Equation http://enlvm.usu.edu/ma/nav/activity.jsp? sid=__shared&cid=emready@eqns_line s&lid=4

23. 3. Write the Equation of the Line Given a Graph HOMEWORK 1. p. 331 (#1-6) 2. p. 331 (#14-18) 3. p. 331 (#23-31) DUE FRIDAY!