1. What is a function?

A function can be defined as a rule which associates the value of a variable quantity to the values of another one in such a way that values of the second variable quantity is uniquely determined by the values of first variable.

2. What is a linear function?

A linear function is a function whose graph takes the form of a straight line.

3. What form does a linear function take? (I.e.,What is the standard mathematical notation of a linear function?)

A linear function takes the form of c=ax+b.

4. What is the formula for determining the slope of a line?

A line having points (x1,y1) and (x2,y2) has a slope (m) equals to

m= y2 – y2

x2 – x1

5. Suppose you have a lemonade stand, and when you charge \$1 per cup of lemonade you sell 60 cups. But when you raise your price to \$1.50 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \”C\” for number of cups, and \”P\” for the price you charge. Assume the function is linear.

We can write this given situation as

C = Pr + q  where r and q are the variables to be found.

60 = r + q ———————— (1)

And                                           30 = 1.5r + r  ———————- (11)

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