Download Warm up - Parkway C-2

Warm up
You will get your test
back at the end of class!
1. What is slope? Where do we use it?
2. What are parallel lines?
3. Solve: a-b if a = 5, b=-2, c=0, d=3
c-d
4. What is the reciprocal of 2/3?
5. Joe was thinking of a number. The product
of his number and 7 was -1. What was Joe's
number?
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3.4 Find and Use
Slopes of Lines
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What is slope....
The slope of a non-vertical line is
the ratio of the vertical change
(rise) to the horizontal change
(run) between any two points on
the line.
Often we will use the letter m to
talk about slope.
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Which axis is the x-axis?
Which axis is the y-axis?
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Slope Equation
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Calculate the slope of:
Red Line
(-8,7)
(5,8)
(10,5)
(-2,5)
Black Line
Blue Line
(3,3)
(10,-2)
(-8,-5)
(7,-5)
Yellow Line
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Negative slope: falls from left to right.
Positive Slope: rises from left to right.
Zero Slope: horizontal
Undefined Slope: vertical
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General Rules:
When counting up or to the right is positive!
When counting down or to the left it is negative.
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Let P(3,4), Q(-3,-4) and R(x,y) be three points in
the coordinate plane.
Find the slopes of PQ, PR, and QR
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Use the graph paper to plot these points:
A(-10,0), B(-2,6), C(-4,-5), D(4,1)
Draw segment AB and CD...
What do you notice??
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Postulate 17: Slopes of Parallel Lines
In a coordinate plane, two nonvertical lines are
parallel iff they have the same slope.
Any two vertical lines are parallel.
We still show that lines are
parallel with our arrows!
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Find the slope of
each line. Which
lines are parallel?
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Warm Up!
October 19/20th
1. Find the slope of the line containing (2,3) and (-3,4).
2. What is the slope of a vertical line?
3. If the slope of a line is -2/3, name a point the line will go through
if it goes through the origin.
4. What is the slope of a line parallel to the line in #1?
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th
Warm up 10/19 &20th/10
1. Find the slope of the line containing (2,3) and (‐3,4). (leave as a
fraction)
2. What is the slope of a horizontal line?
3. If the slope of a line is ‐2/3, name a point the line will go through if
it goes through the origin. (you cannot put a comma in so just type
the numbers next to each other)
4. What is the slope of a line parallel to the line in #1? (leave as a
fraction)
5. What is the slope of a vertical line?
d. None of these
c. Undefined
b. 0
a. 1
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1
1. Find the slope of the line containing (2,3) and (‐3,4).
(leave as a fraction)
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2. What is the slope of a horizontal line?
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3. If the slope of a line is ‐2/3, name a point the line will go
through if it goes through the origin. (you cannot put a
comma in so just type the numbers next to each other)
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4
4. What is the slope of a line parallel to the line in #1?
(leave as a fraction)
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5. What is the slope of a vertical line?
A
1
B
0
C
Undefined
D
None of these
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Plot these points!
A(-1,3), B(5,-6), C(6,1), D(-3,-5)
1. Create Line AB and line CD.
2. What do you notice about these two lines?
3. Calculate the slope of AB and CD. Then
multiply the slopes together, what do you get?
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Postulate 18: Slopes of Perpendicular lines
In a coordinate plane, two nonvertical lines are
perpendicular iff the product of their slopes is -1.
Horizontal lines are perpendicular to vertical lines
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Check up
Put the answers for 1 and 2 in your Senteo!
Line f passes through (4,0) and (8,3), graph f.
1. Find the slope of f what is it (simplified fraction)?
2. What is the slope of a line perpendicular to f (simplified
fraction)?
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1
Find the slope of f what is it (simplified fraction)?
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2
What is the slope of a line perpendicular to f (simplified
fraction)?
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What do we need to graph a line?
• Two points
• Point and slope
• Equation (next section)
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Homework (part 1): you have 10
minutes to work on this
p. 175: 3-6, 7-21 odd
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3.5 Write and graph
equations of lines
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Slope Intercept Form- The general form for
writing an equation
y=mx + b
where m is the slope of the line and b is the
y-intercept.
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Find the slope and y-intercept of the following:
1. y = 3x - 2
2. y = -2x + 5
3. y = (2/3)x - 7
4. y= (-5/4)x + (1/3)
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Write the equation for a line whose
slope is 5 and contains the point (3,-2).
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Write an equation of the line in slope intercept form.
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How would we write the equation of line parallel to y=3x+4, if we
did not care anything other than it was parallel, if we wanted it to
go through (3,2) and be parallel?
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The average lifespan of American women has been tracked, and the
model for the data is y = 0.2t + 73, where t = 0 corresponds to 1960.
Explain the meaning of the slope and y‐intercept.
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Standard form: the equation is written as
Ax+By=C, where A and B are not both zero,
and A, B and C do not have any common
factors.
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Graph the line 2x + 3y = 10
First: Find the intercepts
How would we find the x and y-intercepts?
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Point Slope Form
(not in your book need to know!)
y‐y1 = m(x‐x1) where, m is the slope, and (x1, y1) is a point on the line
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Find the equation of the straight line that has slope m = 4 and passes through the point (–1, –6) in point slope form.
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You can rent DVD's at a local store for $4.00
each. An Internet company offers a flat fee of
$16.50 per month for as many rentals as you
want. How many DVD's do you need to rent to
make the online rental a better buy?
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Homework
p. 184: 1-58
multiples of 3
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3.6 The rest of it!
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The distance from a point to a line is the
length of the perpendicular segment from the
point to the line. This is the shortest distance
from the point to the line.
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Likewise, the distance between two
parallel lines is the length of any
perpendicular segment joining the two lines.
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c
What is the distance
from point A to line c?
d
A
What is the distance
from line c to line d?
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Find the distance between the lines with the equations
y = 1.5x + 9 and −3x + 2y = −1. Express your answer as a decimal
rounded to the hundreths place.
17.1264
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Homework!
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