linear functionfunction where the graph is a linechanges by a constant amount at set intervals
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Linear Function
• Function where the graph is a line
• Changes by a constant amount at set intervals
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Slope a fraction that tells the slant of a line
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• Big slope
• Small slope
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• Positive slope
• Negative slope
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• Zero slope
• Undefined (or infinite) slope
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Slope
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If you know two points on a line, you can find the slope by using this formula:
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Example: Find the slope of the line through (3,5) and (7,10).
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Find the slope of the line through (4,9) and (-1,12)
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Find the slope of the line through (4,9) and (-1,12)
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It’s easy to use slope to graph linear functions.
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If a function is written in the form y = mx + b or f(x) = mx + b …• m (the number by x) is the
slope• b (the number by itself) is the
y-intercept, the place where the line crosses the y-axis.
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EXAMPLE: Graph
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EXAMPLE: Graph
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Graph y = –2x + 3
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Graph y = –2x + 3
The y-intercept is 3
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Graph y = –2x + 3
The y-intercept is 3
The slope is -2 or -2/1
… down 2, over 1
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Graph y = –2x + 3
The y-intercept is 3
The slope is -2 or -2/1
… down 2, over 1
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You can also graph lines by using the intercepts (the places where x and y = 0)
Plug in 0 for each variable, and see what the other one is.
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EXAMPLE:
Graph 2x – 5y = -10
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EXAMPLE:
Graph 2x – 5y = -10
x = 0 … 2(0) – 5y = -10 -5y = -10 y = 2(0,2) is the y-intercept.
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EXAMPLE:
Graph 2x – 5y = -10
y = 0 … 2x – 5(0) = -10 2x = -10 x = -5(-5,0) is the x-intercept.
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EXAMPLE:
Graph 2x – 5y = -10
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Horizontal and Vertical Lines
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Horizontal lines• Slope = 0• … So, can be written in
the form y = 0x + b• This simplifies to just y = b• Whenever an equation
says y = #, the graph is a horizontal line through that number.
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Example:Graph y = -2
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Graph y = 3
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Vertical lines• Slope is undefined• These are the only lines that
CAN’T be written in the form y = mx + b.
• Vertical lines always have equations of the formx = #.
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Graph x = 3
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Graph x = -2
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y = # … horizontalx = # … vertical