WarmUp Write an equation of the line for

Warm-Up � Write an equation of the line for the following situations. Remember the equation for a line: y=mx+b 1. Point (6, -3) and has a slope of -2. 2. Point (-3, 0) and has a slope of ⅓.

Do Now � Write an equation of the line for the following situations. Remember the equation for a line: y=mx+b Point (6, -3) and has a slope of -2. y=mx+b -3=-2(6)+b Substitute -3=-12+b +12 9=b y=mx+b y=-2 x+9 Point (-3, 0) and has a slope of ⅓. y=mx+b 0=⅓(-3)+b 0=-1+b +1 +1 1=b y=mx+b y=⅓x+1 Substitute

Writing Linear Equations Given Two Points Objective : SWBAT write equations for lines given two points. (2. 2. a. ii) D. O. L. : Given 2 MC and 2 CR problems, students will write equations for lines given two points with 80% accuracy. Why: If we know two sets of data points have a linear relationship, creating a linear equation can then help us build a model to further understand additional aspects of that relationship.

Essential Question � How does writing an equation for a line help us make predictions?

Agenda � Warm Up � Review – writing when given slope and y-int � Notes – writing equations given 2 points � Practice – writing equations given 2 points � Matching activity � Real World Practice � DOL

Review Level 1 Writing the equation of a line given slope (m) and -intercept (b) Remember : Slope Intercept Form y = mx + b m = slope b = y-intercept y

Whiteboard Level 1 Writing the equation of a line given slope (m) and y-intercept (b) • Write the equation of a line in slope intercept form if: 1. m = b = -4 okay y = x + (-4) better y = x-4

Level 1 Writing the equation of a line given slope (m) and y-intercept (b) • Use Your Whiteboards to Write the equation of a line in slope intercept form if: 5. m = -1 b = 0 okay y = -1 x + 0 better y = -1 x best y = -x

Review Level 2 Writing the equation of a line given slope (m) and a point (x, y) Example: write an equation of a line with slope of 5 and goes through (3, -2) m=5 (3, -2) Start with y = mx + b Substitute in for the values you have and solve for b -2 = 5(3) +b -2 = 15 + b -15 -17 = b Write the equation (level 1) y = 5 x - 17

Level 2 Writing the equation of a line given slope (m) and a point (x, y) • Use Your Whiteboards to Write the equation of a line in slope intercept form if: 1. m = point (-3, -9) 1: 00 1: 01 1: 02 1: 03 1: 04 1: 05 1: 06 1: 07 1: 08 1: 09 1: 10 1: 11 1: 12 1: 13 1: 14 1: 15 1: 16 1: 17 1: 18 1: 19 1: 20 1: 21 1: 22 1: 23 1: 24 1: 25 1: 26 1: 27 1: 28 1: 29 1: 30 0: 01 0: 02 0: 03 0: 04 0: 05 0: 06 0: 07 0: 08 0: 09 0: 10 0: 11 0: 12 0: 13 0: 14 0: 15 0: 16 0: 17 0: 18 0: 19 0: 20 0: 21 0: 22 0: 23 0: 24 0: 25 0: 26 0: 27 0: 28 0: 29 0: 30 0: 31 0: 32 0: 33 0: 34 0: 35 0: 36 0: 37 0: 38 0: 39 0: 40 0: 41 0: 42 0: 43 0: 44 0: 45 0: 46 0: 47 0: 48 0: 49 0: 50 0: 51 0: 52 0: 53 0: 54 0: 55 0: 56 0: 57 0: 58 0: 59 End y= x - 11

Our objective today Level 3 Writing the equation of a line given two points Step 1 – Find Slope (m) Step 2 – Find y-intercept (b) (level 2) Step 3 – Write Equation (y = mx + b) (level 1)

Level 3 Writing the equation of a line given two points Example: Write the equation of a line that goes through the points: (5, 9) (3, 5) Step 1 – Find m Step 2 – Find b m = 2 (5, 9) or m = 2 (3, 5) 9 = 2(5) + b 5 = 2(3) + b 9 = 10 + b 5=6+b -10 -6 -6 -1 = b Step 3 - Write Equation m = 2 b = -1 y = 2 x - 1

A Good Example Write an equation of a line that passes through the points (1, 6) and (3, -4) y=mx+b m= y 1 -y 2 y= -5 x+b x 1 -x 2 6= -5(1)+b -4= -5(3)+b m= 6−(-4) 6=-5+b -4=-15+b 1– 3 +5 +5 +15 m = 10 11=b -2 m= -5 y=mx+b y= -5 x+11

Another Good Example Write an equation of a line that passes through the points ( -3, 1) and (5, 5) m= y 1 -y 2 x 1 -x 2 m= 1− 5 -3 -5 m = -4 -8 m= 1 or. 5 2 y=mx+b 1=. 5(-3)+b 1= -1. 5+b +1. 5 2. 5 = b y=mx+b 5=. 5(5)+b 5= 2. 5+b -2. 5 = b y=mx+b y=. 5 x+2. 5

Do Again – Good Practice Write an equation of a line that passes through the points ( -1, 1) and (4, 5) m= y 1 -y 2 x 1 -x 2 m= 1− 5 -1 -4 m = -4 -5 m= 4 or. 8 5 y=mx+b 1=. 8(-1)+b 1= -. 8+b +. 8 1. 8 = b y=mx+b y=. 8 x+1. 8 y=mx+b 5=. 8(4)+b 5= 3. 2+b -3. 2 1. 8 = b y=mx+b y=. 8 x+1. 8

Hot Air Balloon Write an equation of a line for the balloon using any points on the table m= y 1 -y 2 x 1 -x 2 m= 14. 5 -39. 1 2– 5 m = -24. 6 -3 m= 8. 2 ft per sec y=mx+b 14. 5= 8. 2(2)+b 14. 5= 16. 4+b -16. 4 -1. 9 = b y=mx+b y= 8. 2 x-1. 9 y=mx+b 39. 1= 8. 2(5)+b 39. 1= 41+b -41 -1. 9 = b y=mx+b y= 8. 2 x-1. 9

Wkst 10: Match the Two Points with the Equation of a Line 1. (-2, 5), (-6, -8) A. y=0. 9 x+. 8 2. (-6, 2), (-4, 11) B. y=3 x-5 3. (-2, -1), (8, 8) C. y=3. 25 x+11. 5 4. (1, 4), (5, -1) D. y=-1. 25 x+5. 25 5. (0, -5), (3, 4) E. y=4. 5 x+29

Match the Two Points with the Equation of a Line - Solutions � (-2, 5), (-6, -8) � y=0. 9 x+. 8 � (-6, 2), � y=3 x-5 (-4, 11) � (-2, -1), � (1, 4), (8, 8) (5, -1) � (0, -5), (3, 4) � y=3. 25 x+11. 5 � y=-1. 25 x+5. 25 � y=4. 5 x+29

Your turn… Pick any two points from the table and write an equation on a post it. Switch with your partner and correct. If you have time, go onto the second table. Think-Write-Share: Your equations might be different. Why? Study Time Class Grade 0 55 0. 5 61 1 67 1. 5 73 2 81 2. 5 89 3 91 3. 5 93 4 95 4. 5 97

The Channel Tunnel The “Chunnel” was designed to create a land travel route between England France allowing trains to travel back and forth under the ocean floor. It is the second largest under water tunnel system in the world measuring 31. 4 miles.

The Channel Tunnel � In order to accomplish this feat, engineers had to dig a tunnel along a chalk marl bed. This layer of sediment gradually declined under the ocean floor to a specific point, leveled out, and rose again to the other side.

The Channel Tunnel �A steeper slope would have dug too deep resulting in harder materials to dig through and a risk to trains not being able to scale the incline. A more gradual slope would eventually pierce the ocean floor layer potentially causing a leak and allowing the tunnel to flood with ocean water

The Channel Tunnel � In order for the engineers to maintain a correct course, a linear equation was necessary to determine the appropriate depth of the tunnel as the tunnel moved out under the ocean floor. What is the linear equation for the first points of tunnel construction. Chunnel Entrance (0 km, 60 m) Sea Level or x-axis 1 st Dig Destination (15 km, -70 m)

The Channel Tunnel Solution m= y 1 -y 2 x 1 -x 2 m= 60−(-70) 0 – 15 m = 130 -15 m= -26 meters 3 kilometers y=mx+b y= -26 (x)+b 3 60= -26 (0)+b 3 60=b y=mx+b y= -26 (x)+60 3

The Channel Tunnel � If the linear equation is: � y= -26 (x) + 60 � 3 � What should be the depth of the tunnel 9 km from the tunnel’s starting point? Chunnel Entrance (0 km, 60 m) Sea Level or x-axis 1 st Dig Destination (15 km, -70 m)

The Channel Tunnel � y= Chunnel Entrance -26 (9) + 60 � 3 � y=-26(3) + 60 � y=-78+60 � y=-18 or 18 meters below sea level (0 km, 60 m) Sea Level or x-axis 1 st Dig Destination (15 km, -70 m)

Essential Question � How does writing an equation for a line help us make predictions?

DOL Part 1 � Write the equations of the lines with the following information: 2. ) point (-6, 5) Slope: 2 a. ) y = 2 x + 17 b. ) y = -6 x + 2 c. ) y = 6/5 x + 2 d. ) y = 2 x + 6/5 3. ) point (-3, 1) point (7, 3) a. ) y = -3 x + 7/3 b. ) y = 7/3 x – 1 c. ) y =. 2 x + 1. 6 d. ) y = 3 x + 7

DOL Part 2 � Write a linear equation for each set of pairs � (3, -2), (6, 4) (2, -2), (3, 2) y=2 x-8 y=4 x-10 Write a linear equation from two points on the following table about the amount of natural sweetener consumed in the U. S. each year Years after 1989 Pounds of Natural Sweeteners 1 2 3 4 5 6 135. 6 138. 2 140. 8 143. 4 146 148. 6 y=2. 6 x+133 Advanced: Make a prediction for the pounds used in 2014.