Question

The equation y=3x-6 and the table describe twi different linear functions Which function had the greatest rate of change? Explain

Answer 1

The rate of change is measured by the slope m.

In case of y=3x-6, the slope is the coefficient of x, that is, the slope m is

`m=3`

Now, in the case of the table, we must find the slope m by choosing two points. The slope formula in this case is

`m=(y_2-y_1)/(x_2-x_1)`

where we chose:

`\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(4,16) \end{gathered}`

Then, by substituting these values into the slope formula, we have

`\begin{gathered} m=(16-9)/(4-2) \\ m=(7)/(2) \\ m=3.5 \end{gathered}`

By comparing the slopes, we can see that the function represented in the table has the greatest rate of chance because 3.5>3