Use similar triangles to determine the slope of the line. Write your answer in fraction form
To determine the slope of the line using similar triangles, we need to find the ratio of the vertical change to the horizontal change between two points on the line.
Let's choose two points on the line, say (x1, y1) and (x2, y2). The slope can be calculated as:
Slope = (y2 - y1) / (x2 - x1)
Now, let's form two similar right triangles with these two points and a third point at a constant vertical distance d from the line. The ratio of the vertical change to the horizontal change in these triangles will be the same as the slope of the line.
Therefore, the slope of the line can be expressed as:
Slope = d / (x2 - x1)
This is the slope of the line in fraction form, where d is the constant vertical distance between the line and the third point.