Notes Chapter 3 Section 6 Write Linear Equations Essential Question WHY are graphs helpful?...

Notes Chapter 3 Section 6 Write Linear Equations

Essential Question WHY are graphs helpful?

Vocabulary: point-slope formCommon Core State Standards: 8.EE.8c

Activity – FSW 3.6

• What you will learn • Take a minute to scan the lesson and predict

two things you will learn about.

• 1. point-slope form• 2. write a linear equation

Give an Example of Each

• Slope-intercept Form

• Standard Form

• And today

• Point-Slope Form

• Real-World Link – The cost for 1,2,3 and 4 people to go to the zoo is shown in the table

• 1. Is the relationship linear? Explain?

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 1. Is the relationship linear? Explain?• Yes, the rate of change is constant for every

pair of points in the table!

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

1 1 1

22-13=9 31-22=9 40-31=9


• 2. What is the slope of the related graph?

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

1 1 1

22-13=9 31-22=9 40-31=9


• 2. What is the slope of the related graph?• Difference in y’s over the difference in the x’s.• 9/1 = 9

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

1 1 1

22-13=9 31-22=9 40-31=9


• 3. Choose an ordered pair then substitute the values in the equation y=mx+b.

•

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 3. Choose an ordered pair then substitute the values in the equation y=mx+b.

• y = m x + b• 22 = 9*2 + b

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 4. Solve for b to find the y-intercept.• 22 = 9*2 + b

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 4. Solve for b to find the y-intercept.• 22 = 9*2 + b multiply 9 times 2• 22 = 18 + b subtract 18 from both sides• 4 = b y-intercept is 4 the point (0,4)

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 5. Write an equation of the line in slope-intercept form (y=mx+b).

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40


• 5. Write an equation of the line in slope-intercept form (y=mx+b).

• m=9, b=4 therefore y = 9x + 4

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

• Real-World Link• 5. Graph the data•

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

• Real-World Link• 5. Graph the data•

Number of people, x

1 2 3 4

Total Cost, y $13 $22 $31 $40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

30

35

40

45

• The point-slope form of a linear equation.

• http://www.mathsisfun.com/algebra/line-equation-point-slope.html

http://www.mathsisfun.com/algebra/line-equation-point-slope.html



• Write an equation in point-slope form for the line that passes through (-2,3) with a slope of 4.

• You have a point (-2,3) you have a slope 4• Plug it into point-slope y – y1=m(x - x1)• y – 3 = 4 (x - -2) then simplify• y – 3 = 4(x + 2)

• Write the slope-intercept form of the equation for the line that passes through (-2,3) with a slope of 4.

• y – 3 = 4 (x - -2) then simplify• y – 3 = 4(x + 2) use the

distributive prop.• y – 3 = 4x + 8• + 3 + 3 add 3 to both

sides• y = 4x + 11 slope-intercept

form

Got It a

• You have 3 minutes to complete Got it problem a Get going!!

• You have a point (-1,2) and a slope -1/2 plug it into point-slope y – y1=m(x - x1)

• y – 2=-1/2(x - -1)• y – 2 = -1/2(x + 1) simplify• y – 2 = - ½*x + ½ use the distributive prop.• + 2 + 2 add 2 to both sides• y = - ½ x + 2 ½ you have slope-intercept form

• Write an equation in point-slope form for the line that passes through (8,1) and (-2,9).

• You have two points all you can find is slope.• m = (1-9)/(8- -2) = -8/10 = -4/5• Now I have a point (8,1) and a slope -4/5 I can

plug it into point-slope y – y1=m(x - x1).

3

• Write an equation in point-slope form for the line that passes through (8,1) and (-2,9).

• Now I have a point (8,1) and a slope -4/5 I can plug it into point-slope y – y1=m(x - x1).

• y – 1 = -4/5 (x – 8) use the distributive prop.• y – 1 = -4/5*x + 32/5• + 1 + 1 add 1 to both sides• y = (-4/5)x + 37/5 you have slope-intercept

Got It c and d

• You have 3 minutes to complete Got it problem c Get going!!

• (3,0) and (6,-3) 2 points – find slope• m = (0 - -3)/(3 - 6) = 3/-3 = -1• Now I have a point (3,0) and a slope -1 so I can

plug it into point-slope y – y1=m(x - x1).• y – 0=-1 (x - 3) use the distributive prop.• y = -1x + 3 you have slope-intercept form

Got It c and d

• You have 3 minutes to complete Got it problem d Get going!!• (-1,2) and (5,-10) 2 points, find slope• m = (2 - -10)/(-1 - 5) = 12/-6 = -2• Now I have a point (-1, 2) and a slope -2 so I can plug it into

point-slope y – y1=m(x - x1).• y – 2=-2 (x - -1) simplify• y – 2 = -2(x + 1) use the distributive prop.• y – 2 = -2x – 2• + 2 + 2 add 2 to both sides• y = -2x you have slope-intercept form

• The cost of assistance dog training sessions is shown in the table. Write an equation in point-slope form to represent the cost y of attending x dog training sessions.

Number of sessions – x Cost - y

5 165

10 290

What do I have?

• Write an equation in point-slope form.

• I have two points I can find slope• m = (165-290)/(5-10) = -125/-5 = 25• Now, I have a point (5,165) and a slope 25, I

can plug it into point-slope y – y1=m(x - x1).


5 165

10 290

• Write an equation in point-slope form.

• Now, I have a point (5,165) and a slope 25 I can plug it into point-slope y – y1=m(x - x1).

• y – 165 = 25(x – 5)

• I am done!!!


5 165

10 290

Got It e

• You have 3 minutes to complete Got it problem e Get going!!

• The cost for making spirit buttons is shown in the table. Write an equation in point-slope form to represent the cost y of making x buttons.

Number of buttons, x

Cost, y

100 25150 35

What do I have?

Got It e

• You have 3 minutes to complete Got it problem e Get going!!• Write an equation in point-slope form to represent the cost y

of making x buttons.• I have two points I can • find slope• m = (25-35)/(100-150) • = -10/-50 = 1/5• Now, I have a point (100,25) and a slope 1/5 I can plug it into

point-slope y – y1=m(x - x1).• y – 25 = 1/5(x – 100)• And I am DONE!!

Number of buttons, x

Cost, y

100 25150 35

• Guided Practice• I will work the odd• You will work the even

• Guided Practice• 1. point (2,5) and slope 4• I have a point and slope so I use point-slope • y – y1=m(x - x1).• y – 5 = 4(x – 2) point-slope• y – 5 = 4x – 8• y = 4x – 3 slope-intercept

• Guided Practice• 3. Janelle is planning a party. The cost for 20

people is $290. The cost for 45 people is $590. Write an equation in point-slope form to represent the cost y of having a party for x people.

• 20 people, 290 cost• 45 people, 590 cost

What do I have?

• Guided Practice• 3. Write an equation in point-slope form • 20 people, 290 cost• 45 people, 590 cost• I have two points I can find slope• m = (290-590)/(20-45)=-300/-25=12 • Now, I have a point (20,290) and a slope 12 I can plug it

into point-slope y – y1=m(x - x1).• y – 290 = 12(x – 20)• And I am DONE!!

• Guided Practice You do the even

• Guided Practice• 2) y-1 = -2(x+3) and y = -2x-5

• 4) is it easier to substitute than to solve?

Homework 3.6

• Independent Practice• Pages 225-226 problems 1-14

Quick Review Given Find

Point & Slope y – y1=m(x - x1)

Slope & y-intercept y = mx + b

Two points – Find slope m= (y2-y1)/(x2-x1)

Notes Chapter 3 Section 6 Write Linear Equations Essential Question WHY are graphs helpful?...

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