Functions of the Form <em>y = mx + c</em>
Functions of the form \(y=mx+c\)
Optional Investigation: The effects of \(m\) and \(c\) on a straight line graph
On the same set of axes, plot the following graphs:
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\(y=x-2\)
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\(y=x-1\)
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\(y=x\)
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\(y=x+1\)
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\(y=x+2\)
Use your results to deduce the effect of different values of \(c\) on the graph.
On the same set of axes, plot the following graphs:
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\(y=-2x\)
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\(y=-x\)
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\(y=x\)
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\(y=2x\)
Use your results to deduce the effect of different values of \(m\) on the graph.
The effect of \(m\)
We notice that the value of \(m\) affects the slope of the graph. As \(m\) increases, the gradient of the graph increases.
If \(m>0\) then the graph increases from left to right (slopes upwards).
If \(m<0\) then the graph increases from right to left (slopes downwards). For this reason, \(m\) is referred to as the gradient of a straight-line graph.
The effect of \(c\)
We also notice that the value of \(c\) affects where the graph cuts the \(y\)-axis. For this reason, \(c\) is known as the \(y\)-intercept.
If \(c>0\) the graph shifts vertically upwards.
If \(c<0\) the graph shifts vertically downwards.
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\(m<0\) |
\(m=0\) |
\(m>0\) |
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\(c>0\) |
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\(c=0\) |
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\(c<0\) |
Table: The effect of \(m\) and \(c\) on a straight line graph.
You can use this Phet simulation to help you see the effects of changing \(m\) and \(c\).
This lesson is part of:
Functions I