linear functions. linear function? for a fixed change in one variable there is a fixed change in the...
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![Page 1: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/1.jpg)
Linear functions
![Page 2: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/2.jpg)
Linear function?
For a fixed change in one variable there is a fixed change in the other variable
Slope stays the same
![Page 3: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/3.jpg)
Linear Function?
x y5 -4
10 -115 220 5
![Page 4: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/4.jpg)
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
![Page 5: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/5.jpg)
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
![Page 6: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/6.jpg)
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
![Page 7: Linear functions. Linear function? For a fixed change in one variable there is a fixed change in the other variable Slope stays the same](https://reader036.vdocuments.mx/reader036/viewer/2022062421/56649dbc5503460f94aae171/html5/thumbnails/7.jpg)
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