Question

Find the slope of the line graphed below.

Answer 1

`\displaystyle (1)/(2)`

Explanation:

Slope describes the rate of change for a line.

Counting Slope

Slope is rise over run. This means that slope is the change in y divided by the change in x. One way we can find this is by counting the changes between the points. For example, mark the points (0,1) and (2,2). Starting at (0,1) count how many units you go up and right. To reach (2,2), you should count 1 unit up and 2 units right. Vertical movement is the change in y and horizontal movement is the change in y. So, the slope is 1/2, because that is the change in y divided by x.

Slope Formula

We can also find slope algebraically. To do this we use the slope formula,
`\displaystyle(y_(2)- y_(1) )/(x_(2)- x_(1) )`. We can plug the same points from above, (0,1) and (2,2), into this formula.

• 
  `(2-1)/(2-0) =(1)/(2)`

Once again, through this method, we find that the slope equals 1/2. Both counting from the graph and the slope formula represent the same idea; they are simply different ways of thinking about slope.