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Information
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Don’t connect 3!
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Drawing graphs of linear functions
The x-coordinate and the y-coordinate in a coordinate
pair can be linked by a function.
What do these coordinate pairs have in common?
(1, –1), (4, 2), (–2, –4), (0, –2), (–1, –3) and (3.5, 1.5)?
In each pair, the y-coordinate is 2 less than the x-coordinate.
These coordinates are linked by the function:
y=x–2
We can draw a graph of the function y = x – 2 by plotting
points that obey this function.
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Plotting graphs of linear functions
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Calculating the slope
If we are given any two points (x1, y1) and (x2, y2) on a line we
can calculate the slope of the line as follows:
y
slope =
change in y
change in x
(x2, y2)
rise
=
run
y2 – y1
(x1, y1)
To help you find this more easily,
you can draw a right triangle
between the two points on the line.
slope =
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x2 – x1
x
y2 – y1
x2 – x1
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Calculating slopes
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The general equation of a straight line
The general equation of any straight line is:
y = mx + b
This is called the slope-intercept
form of a straight line equation.
The value of m tells us the slope of the line.
The value of b tells us where the line crosses the y-axis.
This is called the y-intercept and it has the coordinates (0, b).
For example, the line y = 3x + 4 has a slope of 3 and crosses
the y-axis at the point (0, 4).
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The slope and the y-intercept
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Music download prices
Investigate the cost of these music download services:
Z-Tunes:
No monthly charge.
$0.99 per song
hi-notes:
$12.95 per month,
$0.79 per song
Yes Trax
$9.99 per month
$0.49 per song
MP3 House:
$19.99 per month,
no charge per song
Write the monthly cost of each service as a function of
the number of songs downloaded. Compare the services
with a graph and a table.
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Graphing the costs
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