Question

What is the slope of the function, represented by the table of values below ?

Answer 1

For a given function, slope is defined as the change in outputs, or y-values divided by the change in inputs, or x-values. In essence the slope asks "For a given change in x, how much does y change?" or even more simply: "How steep is the graph of this function?". This can be represented mathematically by the formula:
$m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Since we have a table of x,y pairs it's the last form of that equation that will be the most useful to us. To compute the slope we can use any two pairs, say the first two, and plug them into our formula:
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{4-10}{0-(-2)}=\frac{-6}{2}=-3$

We can check this answer by using a different pair, say the last two:
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{(-23)-(-14)}{9-6}=\frac{-9}{3}=-3$.

As a common sense check: Our y-values get smaller as our x-values get bigger so a negative slope makes sense. 

m=-3