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Warm UPPlease have a blank page ready to start the warm up. You will receive instruction regarding your warm up shortly.
Homework Q&A
Linear Functions: Slope Intercept Form
Objective:
I can write and graph a linear function in slope intercept form
2-3
Slope
x
y
VerticalChange
HorizontalChange
Vertical Change (rise)
Horizontal Change (run)
(x2, y2)
(x1, y1)
Sketch and describe the slopes of each graph.
x
y
Positive Slope
x
y
Negative Slope
x
y
Slope = 0
x
y
undefined
Find the slope for each set of points.
(1,7) and (6, 4)
(-4, -5) and (5, 6)
4 − 76 − 1
¿−35
7 − 41 −6
¿3
−56−(−5)5−(− 4 )
¿119
−5 − 6− 4−5
¿−11− 9
(x1, y1) and (x2, y2):12
12
xx
yy
x
ySlope = m y-intercept = b
Linear Equation: Slope Intercept form
m = 2; y-intercept is (0, -3)
bmxy xy 2 3
m = ; y-intercept is (0, 7)bmxy
xy 3
2 7
3
2
bmxy
-5 5-5
5
x
y
5 10
5
10
x
y
bmxy Linear Equation: Slope Intercept form
xy 2
1 6VerticalChange Horizontal
Change
bmxy
xy 2 3VerticalChange
HorizontalChange
Linear Equation: Slope Intercept form23 xy
5 10
5
10
x
y
5 10
5
10
x
y
Graph:
1. Plot y-intercept2. Use slope to plot 2nd point.3. Draw line through points.
5 10
5
10
x
y
5 10
5
10
x
y
VerticalChange
HorizontalChange
43
2
xyGraph:
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
Writing in slope intercept formSolve for y!
p.78: 9, 11, 13, 15, 18,
19, 23, 27, 29, 33, 35, 44,
47-49
2 𝑥+6 𝑦=24
6 𝑦=− 2𝑥+2466 6
𝑦=−13𝑥+4
9 𝑥− 3 𝑦=12
−3 𝑦=−9 𝑥+12−3−3 −3
𝑦=3 𝑥− 4
Warm UpWhat is the slope and y-intercept in the following equations:
y = 11x +4
3y + 2 = 6x
Find the slope given points: (6,7) and (15,2).
m = 11 y = 4
y 23
Y = m = 2 −𝟐𝟑
2 −715 −6
=−𝟓𝟗
Homework Q&A
More Linear Equations Point Slope Form
Objective:
I can write and graph a linear function in point slope form.
Day 2
Point Slope FormSlope Formula:
12
12
xx
yym
mxx
yy
1
1)( 1xx )( 1xx
Point (2, 3) Slope: 4Examples
) ( xy 23 4
Point (-3, -7) Slope:
) ( xy + 3+ 7
Point (-6, 5) Slope: -2
) ( xy + 65 -2
3
2
3
2Slope
Point(x1, y1)
)( 11 xxmyy
Write an equation given two pointsEquation for the line that passes through (3, 2) and (5, 8)
1. Find the slope.
2. Choose 1 of the given points and substitute into point-slope form.
35
28
m2
6 3
) ( xy 3 32
OR) ( xy 3 58
)3(32 xy )5(38 xy932 xy 1538 xy
73 xy 73 xySam
e Line?
Equation for the line that passes through (7, 3) and (3, 11)
73
311
m4
8
2
)7(23 xy
OR)3(211 xy
Graphing from point-slope formGraph the equation:
)4(3
23 xy
Point: Slope:
-5 5-5
5
x
y
)3 ,4(3
2
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
Graph the equation: )4(
5
22 xy
Point: Slope:
-5 5-5
5
x
y
)2 ,4( 5
2
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
Exit Ticket Today!!!
p.86:10-21, 42-44, 49
Warm Up
Write an example of an equation in:
Y-intercept form
Slope form
Homework Q&A
More Linear Equations Standard Form
Objective:
I can write and graph a linear function in standard form.
Day 3
Standard Form:
Point Slope Form:
Slope-Intercept Form:
Three Forms of a linear equationy = mx + b
y – y1 = m(x – x1)
Ax + By = C
where A, B, and C are integers.- meaning no fractions or decimals.
m = slope b = y-intercept
m = slope (x1, y1) = point
𝑦=23𝑥+5
𝑦− 9=23(𝑥− 6)
2 𝑥−3 𝑦=− 15
Solve for y!
Standard Form to Slope-Intercept Form
No fractionsor decimals
Slope-Intercept Formto Standard Form
Add or Subtract mxfrom both sides.
Multiply to eliminate denominators.
3 𝑥+5 𝑦=15
5 𝑦=− 3𝑥+15𝑦=−
35𝑥+3
𝑦=−75𝑥+3
75𝑥+𝑦=35()
7 𝑥+5 𝑦=15
𝑦=32𝑥+7
3 𝑥− 2 𝑦=− 14−3 𝑥+2 𝑦=14
Ax + By = C
Graphing a standard form equationFind and graph the intercepts.
x-intercept y-intercept
3x + 5y = 15
x = ___________
y = _________
x = y = 3
153
155
5
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
-5 5-5
5
x
y
𝐴𝑥+𝐵𝑦=𝐶𝐴𝑥+𝐵 (0)=𝐶
𝐴𝑥=𝐶𝑥=
𝐶𝐴
𝐴𝑥+𝐵𝑦=𝐶𝐴(0)+𝐵𝑦=𝐶
𝐵𝑦=𝐶𝑦=
𝐶𝐵
A runner is participating in a 10-kilometer road race and she is currently at the halfway point. She looks at her watch and notices that it has taken her exactly twenty five minutes to get to this point. Assume that she has run at a constant rate and will complete the race at this same rate.
Write an equation to represent the distance she has run from where she is now.
x = Time (minutes)
y = Distance from 5 km (km)
Running Rate:
Starting point: 52.0 xy
Slope-intercept Form
min25
5km 2.0
5 (y-intercept)
bmxy
After a water main break, a large building’s basement wasflooded to the ceiling. The local fire department providestwo pump trucks to pump the water out. The first truck canpump 25 cubic feet of water per minute and the second truck canpump 32 cubic feet of water per minute. The building is a rectangular prism, measuring 150 feet long, 120 feet wide and 10 feet deep.
Time spent pumping
x = First Truck
y = Second Truck000,180
If both trucks are used for different amounts of time to pump out the basement, write an equation to represent this situation.
x25 y32
Standard Form
Amount ofwater 1st Truck
+ Amount of water 2nd Truck
= Total
p. 86:22-31, 36-41