Use similar triangles to determine the slope of the line
To use similar triangles to determine the slope of a line, follow these steps:
1. Identify two similar triangles formed by the line and any other lines or shapes on the graph.
2. Determine the corresponding sides of the similar triangles.
3. Find the ratio of the corresponding sides.
4. The ratio of the corresponding sides represents the ratio of the corresponding lengths in the two triangles.
5. The slope of the line can be determined by taking the ratio of the corresponding sides that represent the change in y-coordinates to the corresponding sides that represent the change in x-coordinates.
For example, if you have two similar triangles with corresponding sides:
Triangle 1: Side A with length 4 and Side B with length 6
Triangle 2: Side A with length 2 and Side B with length 3
To find the slope of the line, determine the ratio of the corresponding sides:
Ratio of A: 4/2 = 2
Ratio of B: 6/3 = 2
Since the ratio of the corresponding sides is 2:2, we can simplify it to 1:1. Therefore, the slope of the line is 1.