Question

Identify the slope (rate of change) of the following table or graph.

Answer 1

5

Explanation:

Slope describes the rate of change for a specific function.

Defining Slope

The slope of a table describes the rise over run. This means that the slope is the change in y over the change in x. The slope is also called the rate of change, specifically the change in y per x.

Since the function described in the table is linear, we know that the slope will be constant throughout the entire function. This means that we can use any of the points to solve for slope because it does not change.

Slope Formula

One way to find the slope is through the slope formula. The slope formula is as follows:

• 
  `\displaystyle (y_(2)- y_(1) )/(x_(2) -x_(1) )`

So, all we need to do is plug in any two coordinate points from the table. One pair we can use is (1, 5) and (2, 10).

• 
  `\displaystyle (10-5)/(2-1)=5`

This means that the slope is 5.