Transcript Equations of Lines Lesson 2.2 (x2, y2) • m Point Slope Form   We seek the equation, given point and slope Recall equation for calculating slope, given.

Equations of Lines
Lesson 2.2
(x2, y2)
•
m
Point Slope Form


We seek the equation, given point and slope
Recall equation for calculating slope, given two
points
y1  y2
x1  x2

m
Now multiply both sides by (x1 – x2)
y1  y2  m  x1  x2 

Let any point (x,y) on the line be one of the points in
the equation
y  y2  m  x  x2 
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Point Slope Form

Alternative form

Try it out …
y  m  x  x1   y1
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For a line through point (6, -2) and slope m = -3/4
determine the equation.
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Show both forms
(6, -2)
•
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Slope Intercept Form
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Recall that we have used
The b is the y-intercept
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y=m*x+b
Where on the y-axis, the line intersects
m is the slope
Given slope
Observe
y-intercept
m
2
3
2
y  x5
3
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Converting Between Forms

What does it take to convert from
point slope form
y  m  x  x1   y1
to slope-intercept form?
y  m x  b
Multiply through the (x – x1) by m
 Simplify the expression
Note that this also
determines the value for the
2
 Try it
y
y-intercept, b
 x  17   4
7
5

Two Point Form

Given (3, -4) and (-2, 12),
determine the equation

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Find slope
Use one of the points in the
point-slope form
y1  y2
y
 x  x1   y1
x1  x2
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Parallel Lines
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Given the two equations
y = 2x – 5
y = 2x + 7
Graph both equations
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Set the style of one
of the equations to
Thick
How are they the same?
How are they different?
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Parallel Lines
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Different: where they cross the y-axis
Same: The slope
Note: they are parallel
Parallel lines have the same slope
Lines with the same slope are parallel
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Perpendicular Lines
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Now consider
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Graph the lines
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2
y  x5
3
3
y   x5
2
How are they different
How are they the same?
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Perpendicular Lines

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
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Same: y-intercept is the same
Different:
slope is different
Reset zoom
for square
Note lines are
perpendicular
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Perpendicular Lines
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Lines with slopes which are negative reciprocals
are perpendicular
Perpendicular lines have slopes which are
negative reciprocals
2
y  x5
3
3
y   x5
2
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Horizontal Lines
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Try graphing y = 3
What is the slope?
How is the line slanted?
Horizontal lines have slope of zero
y = 0x + 3
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Vertical Lines
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•
Have the form
k
x=k
What happens when we try to graph such a
line on the calculator?
Think about
y1  y2 n

x1  x2 0
We say “no slope” or “undefined slope”
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Assignment
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Lesson 2.2A
Page 88
Exercises 1 – 73 EOO
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Direct Variation

The variable y is directly proportional to x when:
y=k*x
• (k is some constant value)
 Alternatively
y
k
x
 As x gets larger, y must also get larger
• keeps the resulting k the same
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Direct Variation

Example:
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The harder you hit the baseball
The farther it travels
Distance hit is directly
proportional to the
force of the hit
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Direct Variation

Suppose the constant of proportionality is 4

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Then y = 4 * x
What does the graph of this function look like?
Note:
• This is a linear function
• The constant of
proportionality is the slope
• The y-intercept is zero
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Applications
Math whiz Horatio Al-Jebra rides a bicycle on a
straight road away from town.
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The graph shows his distance y in miles from town
after x hours
How fast is he riding?
Find y  m  x  b
How far from town
initially
How far from town
after 3 hours and 15 min.
Distance (miles)
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Assignment
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Lesson 2.2B
Page 109
Exercises 75 – 109 EOO
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