8/18/2016
Lesson 1.4
SWBAT
•Write and evaluate linear
equations in slope-intercept
or point-slope form when
given a slope and an
intercept, two points, or a
point and a slope.
History of Men’s 100 meter sprint
8/18/2016
Agenda
•Do Now
•Lecture
•Guided Practice
•Independent Practice
•Exit Ticket
•Closing
III. Linear Functions
A. Definition – a function whose graph is a line
1. Represented with a linear equation
a) Example: y = 3x +2 or f(x) = 3x + 2
2. Need y-intercept & slope to make equation
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B. Intercepts
1. Y-intercept – point at which the line crosses y-axis
(0, y)
2. X- intercept – point at which the line crosses the xaxis (x, 0)
a) How to find the x-intercept?
y-intercept
(0, 2)
x-intercept
(- , 0)
C. Slope – ratio of vertical change to corresponding
horizontal change
1. Slope formula
slope=
(
(
• Basically
)
)
=
, where
-
0
a. Example: (-1, -1) and (0, 2) Find the slope.
=3 +2
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right 1
Rise +3
(change in y)
(0, 2)
Up 3
Run +1
(change in x)
= = 3 = slope
Up 2
=3 +2
Up 1
(-1, -1)
D. Linear Equations (ways they can be written)
1. Standard Form:
+
a. Where A, B, and C are real numbers
b. And A and B are not both zeros
2. Point-slope form:
=
a. m = slope
b. ( , ) is a point on line
3. Slope-intercept form:
a. m = slope
b. b = y-intercept
=
(
+
)
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E. Using different forms for different givens
1. Given slope (m) and y-intercept (b) 
slope intercept form
Given: m = 2, y-intercept = 7
 Substitute into y = mx +b
Given: same slope as
1
y= x 2
4
with y
=2 +7
=
intercept of
=
+
2
3
1
2
+
4
3
2. Given slope (m) and point  either slope intercept form =
or point-slope form
= (
Given: m = 6 and (3, 4)
Using point-slope form
= (
)
.
4 = 6(
3)
simplified to
=6
14
Given: m = -2 and (1,-6)
Using slope intercept form
=
+
b = -4
m= -2
Substitute
= 2
4
+
)
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3. Given 2 points ( ,
)
( ,
a) Must find slope using
(2,4) (3,9)
.
=
9
3
=
)
(4,7) (1,5)
4 5
=
2 1
m=
m=5
b) After finding m, substitute an ordered pair into
point-slope form
= (
)
c) Then simplify into slope-intercept form y =mx+b
(2,4) (3,9)
.
= 5, (2, 4)
4=5
2
=5
2 +4
=5
10 + 4
=5
6
(4,7) (1,5)
m=
, 4, 7
y = x +4
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Agenda
•Do Now
•Lecture
•Guided Practice
•Independent Practice
•Exit Ticket
•Closing
Guided Practice: 1-minute head start
Write the equation in slope intercept form for a line with:
1. Slope (m)&
y-intercept (b)
m=1
b=
2. Point & slope
m =1
Point: (0,8)
3. Two Points
(-3, 9) (8,5)
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Independent Practice 15 minutes
• Silently and independently: if you have a
question, raise your hand. If I am speaking
with another student, you may quietly ask
your elbow partner
• When complete, raise your hand. I will
come by to take a look.
INDEPENDENT PRACTICE: silently and
independently
Slope (m)& yintercept (b)
Point and slope
1.Slope:
Y-intercept: 4
2. Slope: -1
Y-intercept:1000
5. Slope: 3
Point: (1, 5)
4. Slope: 9
Y-intercept: 0
8. Slope: 5
Point: (0,2)
3. Slope: 0.4
Y-intercept: -0.8
6. Slope:
Point: (22, 12)
7. Slope: 1
Point: (-4,1)
Two Points
9. (-3,5) (4,5)
10. (-5,-7) (0,10)
11. (1,2) (2,3)
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INDEPENDENT PRACTICE: Check!
Slope (m)& y-intercept (b)
Point and slope
Two Points
1.Slope:
Y-intercept: 4
5. Slope: 3
Point: (1, 5)
9. (-3,5) (4,5)
2. Slope: -1
Y-intercept:1000
6. Slope:
Point: (22, 12)
5
=
6
7. Slope: 1
Point: (-4,1)
10. (-5,-7) (0,10)
=
2
+4
3
=
+ 1000
3. Slope: 0.4
Y-intercept: -0.8
= 0.4
4. Slope: 9
Y-intercept: 0
=9
Agenda
0.8
=3 +2
=
8. Slope: 5
Point: (0,2)
19
3
3
=5 +2
•Do Now
•Lecture
•Guided Practice
•Independent Practice
•Exit Ticket
•Closing
=5
=
17
+ 10
5
11. (1,2) (2,3)
=
+1
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Exit Ticket: silently and
independently. You have 5 minutes
1. Slope: 5 (0,6)
2. Slope: ½ (4,7)
3. ( , 2) (5,9)
Agenda
•Do Now
•Lecture
•Independent Practice
•Exit Ticket
•Closing