SLOPE of A LINE. Slope What is slope? Why do we want to know? Look at the relationship between rise...
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Transcript of SLOPE of A LINE. Slope What is slope? Why do we want to know? Look at the relationship between rise...
![Page 1: SLOPE of A LINE. Slope What is slope? Why do we want to know? Look at the relationship between rise and run in each of the lines. That would define the.](https://reader036.fdocuments.us/reader036/viewer/2022081515/56649d835503460f94a6a222/html5/thumbnails/1.jpg)
SLOPE of A LINE
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Slope• What is slope?• Why do we want to know?• Look at the relationship between rise and run in each of the lines. That would define the slope of the line.
X
y
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Look at the relationship between the blue arrow and the red arrow
Line 1
Line 2
Line 1 Line 2
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=
Rise (↕)
Run (↔)
Difference in the y coordinate
Difference in the x coordinate
1
2
What is the slope of this staircases?
- 1
2
SLOPE
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Practice Problems
#1
#2
#3
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Draw three different staircases that have a slope of 3/2. Label the riser and runner for each staircase.
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What is the slope of this staircase?
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What is the slope of this line?
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A B
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CHALLENGE PROBLEM:
Draw a line with a slope of 3/1. Can you draw more than 1?
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Slope Practice
A B
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Order these staircases from flattest to steepest (#1 is the flattest, #2 is the next flattest). If two staircases have the same slope, give them the same number.
A B C D
E F G
{ F, C, E, A/D, G, B }
{ .4, .666, .75, 1/1, 1.666, 4 }
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Special cases
Horizontal Line
m= 0
Vertical Line
m = undefined
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Finding the slope given two points
Find the slope of the line that passes through (2, 3) and (4, -1)
Two ways to do this:a) With a pictureb) With a formula
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Two ways:a) Do it on a graphb) Formula: m = y2-y1
x2-x1
Find the slope through (3, 2) and (-1, 5)
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Find the slope of the lines that contain the following
points
a) (1, 0) and (-2, 1)
a) (2, 3) and (5, -2)
a) (3, 3) and (1, -1)
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The slope is the coefficient of x (you might have to solve for y first)
Find the slope of the these equations:
a) y = -2x + 1 m =
b) 3y + 2x = -9 m =
c) x - y = 4 m =
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Equations of lines in slope intercept formy = mx + b
m = slope is the number next to x (the coefficient of x)
b = the y-intercept (the point where the lines crosses the y-axis)
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Find the slope and the y-intercept
€
y =3
5x + 2
y = 2x −2
y = x
m y-int
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To graph using the slope and y-intercept
1) Start on the y-axis at b
2) Use the slope m to draw the triangle (you need a fraction here)
• Positive m - up and right • Negative m - down and right
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€
y =2
3x − 4
y = 3x +1
y = −x
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Use the slope and y-intercept to graph lines
€
2x + y = 3
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Drawing a Line with One Point & The Slope
Draw the line that passes through (-1, -3) & has Slope = 4/2
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Example #2. Point (-4, 3) & Slope = -3/2
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Slope: slope m =
1. To find slope from two points: use the formula or draw the two points and draw the
triangle.
2.To find slope from a graph: draw the triangle (you need to choose two points on the line first)
3.To find slope from an equation - solve for y first, the slope is the coefficient of x.
Parallel Lines: they have the same slopePerpendicular Lines - slopes and opposites and reciprocals from each other
€
rise
run
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Sketching Lines
To sketch a line you need to know:
A) direction: given by the sign of m
B) steepness: given by the absolute value of m
C) where it hits the y-axis: given by b
Pos neg
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Sketch and describe the line
y = 2x - 1 3x + 2y = 4
x = -2 y = 0 y = -5x€
y =1
3x + 2
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Parallel lines
Have the same slope.
Are these lines parallel?a) You need the slope mb) You might have to solve for y
first.
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Perpendicular Lines
Triangles I drew to find slope
They are the same - just rotatedThe run of the first is the ____of the second one.The rise of the first is the ____of the second one.
If the slope of the first one is mThe slope of the second one is_____
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1) Are the following lines perpendicular, parallel or neither?
y = 3x + 2 and y = -3x + 4y = 3x + 2 and y = 1/3 x + 2y = 3x + 2 and y = -1/3 x + 2y = 3x + 2 and y = 3x - 5
2) Find the slope of the line perpendicular and parallel to the graph of each line:
y = 3/2 x + 7y = 12x + y = 3y = 3x - 2