1. Linear functions

2. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same

3. Linear Function? xy 5-4 10 152 205

4. We can do this for all of the data points, but easier to do in excel…

5. Linear Functions If the rate of change is constant (the same) between data points the function is linear ABC 1xyRate of Change 2 5-4 3 10 =(B3-B2)/(A3-A2) 4 152 5 205

6. Calculating the y intercept “b” ABC 1xy Rate of Change 2 5-4 3 10 0.6 4 152 0.6 5 205 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

7. Practice – Which functions are linear? xy 11 23 59 713 xy 21 75 911 1217 xy 220 413 66 8 xy 311 516 721 926 1131