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Notes Chapter 3 Section 6
Write Linear Equations
Essential Question
WHY are graphs helpful?
Vocabulary: point-slope form
Common Core State Standards: 8.EE.8c
Activity – FSW 3.6
Page 221
• 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
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 1. Is the relationship linear? Explain?
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
1
Total Cost, y $13
22-13=9
2
1
$22
31-22=9
3
1
$31
4
$40
40-31=9
• 1. Is the relationship linear? Explain?
• Yes, the rate of change is constant for every
pair of points in the table!
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
1
Total Cost, y $13
22-13=9
2
1
$22
31-22=9
3
1
$31
4
$40
40-31=9
• 2. What is the slope of the related graph?
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
1
Total Cost, y $13
22-13=9
2
1
$22
31-22=9
3
1
$31
4
$40
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
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 3. Choose an ordered pair then substitute the
values in the equation y=mx+b.
•
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 3. Choose an ordered pair then substitute the
values in the equation y=mx+b.
• y=mx+b
• 22 = 9*2 + b
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 4. Solve for b to find the y-intercept.
• 22 = 9*2 + b
Page 221
• Real-World Link – The cost for 1,2,3 and 4 people
to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
•
•
•
•
2
3
4
$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)
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 5. Write an equation of the line in slopeintercept form (y=mx+b).
Page 221
• Real-World Link – The cost for 1,2,3 and 4
people to go to the zoo is shown in the table
Number of
people, x
1
Total Cost, y $13
2
3
4
$22
$31
$40
• 5. Write an equation of the line in slopeintercept form (y=mx+b).
• m=9, b=4 therefore y = 9x + 4
Page 221
• Real-World Link
• 5. Graph the data
•
Number of
people, x
1
2
3
4
Total Cost, y
$13
$22
$31 $40
Page 221
• Real-World Link
• 5. Graph the data
•
Number of
people, x
1
2
3
Total Cost, y
$13
$22
$31 $40
45
40
35
30
25
20
15
10
5
0
0
1
2
3
4
5
4
Page 222
• The point-slope form of a linear equation.
• http://www.mathsisfun.com/algebra/lineequation-point-slope.html
Page 222
• 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)
Page 222
• 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
Page 222 – 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
Page 223
• 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).
Page 223
• 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)
• y – 1 = -4/5*x + 32/5
• +1
+1
• y
= (-4/5)x + 37/5
use the distributive prop.
add 1 to both sides
you have slope-intercept
Page 223 – 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
Page 223 – 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
Page 224
• 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?
Page 224
• Write an equation in point-slope form.
Number of sessions – x
Cost - y
5
165
10
290
• 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).
Page 224
• Write an equation in point-slope form.
Number of sessions – x
Cost - y
5
165
10
290
• 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!!!
Page 224 – 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
25
150
35
What do I have?
Page 224 – 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.
Number of
Cost, y
buttons, x
• I have two points I can
100
25
• find slope
150
35
• 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!!
Page 224
• Guided Practice
• I will work the odd
• You will work the even
Page 224
• 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
Page 224
• 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
What do I have?
• 45 people, 590 cost
Page 224
•
•
•
•
•
•
•
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!!
Page 224
• Guided Practice You do the even
Page 224
• 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)