Use similar triangles to determine the slope of the line. What’s the answer
The slope of a line can be determined by comparing the vertical change (rise) to the horizontal change (run) between two points on the line. Using similar triangles, we can compare the rise and run between two points to find the slope.
Let's say we have two points on the line: (x1, y1) and (x2, y2).
The rise between the two points is y2 - y1, and the run is x2 - x1.
Now, we can set up a proportion with the rise and run of our two points and the rise and run of our similar triangles:
(y2 - y1) / (x2 - x1) = (y - y1) / (x - x1)
Simplifying the proportion, we get:
(y2 - y1) / (x2 - x1) = (y - y1) / (x - x1)
The slope of the line is equal to the ratio of the rise to the run:
Slope = (y2 - y1) / (x2 - x1)
So, by using similar triangles, we have determined the slope of the line.