Honors Geometry Companion Book, Volume 1

3.2.1 Finding the Slope Given Two Points (continued)

Example 2 Again, to find the slope of a line, substitute the coordinate values from two points on that line into the slope formula and simplify. When the graph of a line is given, the slope formula can still be used to find the slope of the line. Simply identify two points on the line and then substitute their coordinates into the formula.

Consider this exercise. Begin by choosing any two points on the line. Here, the points ( − 1, − 2) and (3, 4) are identified. Substitute the coordinates into the slope formula. The slope is found to be 3/2. Note that different points could have been used to find the slope. Find the slope of this line again, but now use the points (1, 1) and (3, 4). 3 2 As expected, the same slope is found. Notice that the process was simpler this time because there was no need to simplify the fraction. = − − 4 1 3 1 = m

Remember, a table is a list of x - and y -values that form coordinate pairs. In other words, a table is a list of points.

In this exercise, it is given that the table describes a linear relationship. This means that the points on the table will form a straight line. Once again, the slope formula can be used. Choose any two points from the table, substitute their coordinates into the formula, and simplify. Since this is a linear relationship, it does not matter which two points are chosen from the table.


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