The linear equation

ψ=aχ+b

 

Any time you have a "ψ equals a number" equation (i.e. y=5, with no x in it), the graph will always be a horizontal line.

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Any time you have an equation as ψ=aχ+b with a<0, then its graph is a straight line  and the corresponding function f(x) = aχ+b is decreasing.

Changing the value of a, the angle between the x-axis and the straight line is changing.
Have a look at Excel file: y=-aχ+b.xls (Click here)
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Any time you have an equation as ψ=aχ+b with a>0 , then its graph is a straight line and the corresponding function f(x) = aχ+b is increasing.

Changing the value of b, the straight line is moving from left to right and vice versa across the axis x, changing the y-intercept.

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WORK

1. Have a look at the Excel file revised y=aχ+b.xls (Click here) and move the scrollbar in order to change the value of a and b.
What do you remark?

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2. Go to the sheet Sales of the same excel file.

What's about the line in the graph?

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3. Look at the Geogebra application (Click here)

Which is the straight line that shows that you have bought cheaper  and why?
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