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Linear functions
Linear function?
For a fixed change in one variable there is a fixed change in the other variable
Slope stays the same
Linear Function?
x y5 -4
10 -115 220 5
change in y
change in xm
We can do this for all of the data points, but easier to do in excel…
1 ( 4) 30.6
10 5 5m
2 ( 1) 30.6
15 10 5m
Linear Functions
If the rate of change is constant (the same) between data points the function is linear
A B C
1 x y Rate of Change
2 5 -4
3 10 -1 =(B3-B2)/(A3-A2)
4 15 2
5 20 5
Calculating the y intercept “b”
A B C
1 x yRate of Change
2 5 -4
3 10 -1 0.6
4 15 2 0.6
5 20 5 0.6
Choose one set of x and y values We’ll use 20 and 5
Rate of change = m m=0.6
Plug values into y=mx+b and solve for b 5=0.6(20) + b 5=12 + b -7=b
So the linear equation for this data is:
y= 0.6x -7
Practice – Which functions are linear?
x y
1 1
2 3
5 9
7 13
x y
2 1
7 5
9 11
12 17
x y
2 20
4 13
6 6
8 -1
x y3 115 167 219 26
11 31