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