Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?
Step One: Identify two points on the line. In this example we are given two points, (15, 8) and (10, 7), on a straight line.
Step Two: Select one to be (x1, y1) and the other to be (x2, y2). It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).
Step Three: Use the equation to calculate slope. Once we've completed step 2, we are ready to calculate the slope using the equation for a slope:
We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope:
We get the same answer as before!
Often you will not be given the two points, but will need to identify two points from a graph. In this case the process is the same, the first step being to identify the points from the graph. Below is an example that begins with a graph.
A multiplication expression that is translated by the direct translation method is shown in Example 11. The expression translates to x × 15. Some multiplication keywords, such as DOUBLE, TWICE, and TRIPLE, translate into a number and the operation of multiplication, as shown in Examples 12 and 13.
