Question

Writing Linear Equations Using Similar Triangles
On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7.

Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).

What is the ratio of the rise to the run in the smaller triangle in the diagram?
What is the ratio of the rise to the run in the larger triangle in the diagram?
What is the equation of the line in slope-intercept form?

Answer 1

- Ratio of rise to run in the smaller triangle: 2/3 (or 2:3).
- Ratio of rise to run in the larger triangle: 5/7 (or 5:7). Note 5/7 ≠ 2/3, so the larger triangle as given is not similar to the smaller one.
- Equation of the line (slope 2/3 through (0,3)): y = (2/3)x + 3.