6.3Linear Functions: The Equation y = mx + c
Recall: Chapter 5.1 (Linear Equations), the balancing principle used to rearrange an equation into .→A linear function has the form : since the highest power of is 1, its graph is always a straight line. The constant sets the steepness; the constant sets where the line crosses the -axis.
- is the gradient: positive means the line rises, negative means it falls, zero means it is horizontal.
- is the -intercept: the value of when .
- The further is from zero, in either direction, the steeper the line.
Reading gradient and -intercept
State the gradient and -intercept of the line .
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Comparing with :
Gradient
-intercept
Since , the line falls from left to right.
Now you try
State the gradient of .
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Comparing with , gradient
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Rearranging to find gradient and -intercept
Find the gradient and -intercept of the line .
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Gradient , -intercept .
Now you try
State the -intercept of .
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This is a horizontal line with gradient .
The -intercept is .
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