https://file.aiquickdraw.com/mathbot/file/1729890727760aa4tk5ci.jpg

To determine the slope of the line using similar triangles, we can use the concept of "rise over run." The slope \( m \) of a line is calculated as:

\[
m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}
\]

From the graph, let's use two points on the line: 

- (0, 0) and (1, 2)
  
The rise is the change in the \( y \)-value: 
\[
\Delta y = 2 - 0 = 2
\]

The run is the change in the \( x \)-value: 
\[
\Delta x = 1 - 0 = 1
\]

Thus, the slope using these points is:
\[
m = \frac{2}{1} = 2
\]

This means the slope of the line is 2.

Would you like more details or have any questions?

Here are some related questions you might want to consider:
1. How do you calculate the slope between any two given points on a line?
2. What does the slope of 2 represent geometrically on the graph?
3. Can the slope be calculated with other points on this line?
4. What is the importance of using similar triangles for slope calculation?
5. How does the slope affect the steepness and direction of a line?

**Tip:** The slope of a line is consistent, meaning you can use any two points along the line to calculate it, and the value will always be the same.

Use similar triangles to determine the slope of the line.

Learn how to determine the slope of a line using similar triangles and the rise-over-run method. This problem provides a detailed explanation using coordinate geometry and is ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation