today we will: create linear equations from a context and...
TRANSCRIPT
Math 8C
U2D11
Today We will:
Create linear equations from a context and model with tables and
graphs.
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A quick review: Plotting Points
• Plot the pointsA(2, 3)
B(-1, -4)
C(-3, 3)
D(4, -2)
A
B
C
D
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Plotting Points
• Write the ordered pair that corresponds to point B.
• Now do the same for pointsA, C, & D
(5, 4)(-3,4)
(3, -4)
(-4, -3)
(-2, 1)
(1, -2)
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Example• There are $500 in Holly’s bank account. Every month she takes
$50 out, but does not make any deposits.– Make a table of values.
– Make a graph.
– Write an equation.
– Equation: ______________________________
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Example• A rental car company charges an initial fee $50 and then $0.20
for each mile it is driven.– 1st, make a table of values and a graph to represent total cost.
– 2nd, write an equation to represent total cost C, in terms of miles, m
– Equation: ______________________________________
Miles Cost
0
200
400
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You Try!• Lin is tracking the progress of her plant’s growth. Today the plant
is 5 cm high and she knows that plant will continue to grow 1.5 cm each day.– Make a table of values for 0-5 days.
– Make a graph (don’t forget to label your axes and scale!)
– Write an equation that represents the plant’s growth per day.
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You Try!!
• A taxi ride has a flat fee of $3.50 and a charge of $1.50 for every mile travelled.
– a) Write an equation to represent the total cost
– b) How much would you expect to pay for a trip of 15 miles?
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Independent Practice
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Due Today!
Also, please get me your requests to reassess ASAP as the term ends in three
weeks!
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Math 8C
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Today We will:
Compute Slope
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What did you notice about…
• On yesterday’s practice:
– What did you notice about where the line crossed the y-axis?
– What did you notice about the steepness of the line and one of the numbers in your equation?
– What did you notice about the shape of each line? Straight? Curved? Crooked?
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Linear Equations
• A linear equation is an equation whose graph is a straight line. Every point on the line is a solution of the equation.
• These equations can be written in the form
where m is the slope of the line, and b is the y-intercept of the line.
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bmxy
Example
• From yesterday:
– The equation that represented Paulina’s bank account savings was
– What is the slope of the line?
– What is the y-intercept?
– What do these values represent for Paulina?
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350150 mS
150slope
350 intercepty
What is slope?
• Slope is a rate of change.
• Slope is the steepness of a line.
• How do we measure slope?
– How steep is this line?
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Slope Formula
•
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run
rise
xinchange
yinchangeslope
3
4
run
rise
Find the slope of each line
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Slope of line a=
Slope of line b=
Slope of line c=
Slope of line d=
2
1
2-
0
undefined0
2
If given only two points on a line…
• We know that slope is
• So, if given (-2,4) and (4, 12), find the change in y and in x.
• Slope =
xinchange
yinchange
3
4
6
8
xinchange
yinchange
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Formula!
• If given two points )y,(xand)y,(x 2211
12
12
xx
yyslope
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Example
• Find the slope of the line crossing through each pair of points:
– (8, 10), (3, 20)
– (-2, 4), (9, -7)
– (6, -2), (6, 11)
– (5, -1), (1, -1)
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Independent Practice
U2D12 - ICP
Math 8C
U2D13
Today We will:
Create linear equations from a context and model with tables and graphs.
Compare linear equations of the form 𝑦 = 𝑚𝑥 with equations of the form
𝑦 = 𝑚𝑥 + 𝑏.
Compare and contract linear functions represented differently.
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Warm Up
• Sudzo Wash and Wax charges customers $0.75 per minute to wash a car. Write an equation that relates the total charge C to the amount of time t in minutes.
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Practice
• What does this graph show?
• Write the equation of the line shown on the graph.
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Graphing Lines
• What do we need to know about a line in order to graph it?
– Slope
– A point on the line
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Equations in Slope-Intercept Form
When equations are in Slope-Intercept form, we have the slope and a point!
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• The y-intercept is a point on the y-axis, with ordered pair (0, b)
Equations in Slope-Intercept Form
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• When equations are in Slope-Intercept form, we are given the slope and a point on the y-axis.
• Example
– Graph y = 3x + 2
Slope y-intercept
Equations in Slope-Intercept Form
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• Where do we start when graphing a line?
• Example
– Graph y = 3x + 2
– 1st plot the y-intercept
– 2nd use slope to finda second point.
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛=
+3
+1
– Last, connect dots to draw the line
Slope y-intercept
Graph Each Line
• 𝑦 = 2𝑥 − 2
• 𝑦 = −𝑥 + 1
• 𝑦 =2
5𝑥 + 3
• 𝑦 = −1
3𝑥 − 1
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Warm UpMarty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed.
Identify the variables in this situation: x= _____________ y=_____________
What is the given information in this problem (find all that apply)?
y-intercept ________ slope _____ one point ( , ) second point ( , )
a) What amount of money did he begin with?
b) Write an equation for the situation.
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Find the slope
4.
5.
1. (2, 1), (3, 6)
2. (-2, -2), (-7, -7)
3. (2, 1), (2, -7)
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Graph Each Line
• 𝑦 = 3𝑥 −1
• 𝑦 = −𝑥
• 𝑦 =4
5𝑥 − 3
• 𝑦 = −5
2+ 2
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What about these weird ones?
• How would you graph something like 𝑦 = 2?
– This equation says that y can only ever be 2, regardless of what x is.
• How about something like 𝑥 = −3?
– This equation says that x can only ever be -3, no matter what y is.
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Graph 𝑦 = 2
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Graph 𝑥 = −3
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You Try!
• State the slope and the y-intercept of each line. Then graph the line of each equation:
1. 𝑦 = 2𝑥 − 3
2. 𝑦 = −1
3. 𝑦 = −3
4𝑥 + 1
4. 𝑥 = 5
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Independent Practice
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Heads Up!
Quiz on Monday(FA)
There will be a Summative Assessment on
D11-D14 next week.
Math 8C
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Today’s Quiz:Construct viable arguments and critique the
reasoning of others.
Interpret the results of mathematics in terms of the context in which it was presented.
Create linear equations from a context and model with tables and graphs.
Compare linear equations of the form 𝑦 = 𝑚𝑥with equations of the form
𝑦 = 𝑚𝑥 + 𝑏.
Compute slope.
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