https://file.aiquickdraw.com/mathbot/file/17297221119768q31n9q5.jpg

The graph shows a straight line passing through the origin, which suggests a proportional relationship between \(x\) and \(y\). To find the equation of this line, we need to determine its slope, since the line passes through the origin and follows the form \(y = mx\), where \(m\) is the slope of the line.

### Steps:
1. **Find two points on the line**: From the graph, the line passes through the points \((0, 0)\) and \((10, 5)\).
   
2. **Calculate the slope \(m\)**:
   \[
   m = \frac{\Delta y}{\Delta x} = \frac{5 - 0}{10 - 0} = \frac{5}{10} = \frac{1}{2}
   \]
   
3. **Write the equation**: Since the slope is \(\frac{1}{2}\), the equation of the line is:
   \[
   y = \frac{1}{2}x
   \]

This is the equation that represents the proportional relationship in the graph.

Let me know if you'd like more details or if you have any other questions!

Here are 5 related questions:
1. What does it mean for a relationship to be proportional in terms of a graph?
2. How does the slope of a line relate to the steepness of the graph?
3. What would the equation look like if the slope was negative?
4. Can proportional relationships ever have intercepts other than the origin?
5. How do you calculate slope when the line passes through non-integer points?

**Tip**: Always remember that for a proportional relationship, the graph will pass through the origin (0,0), and the equation will always be in the form \(y = mx\).

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Learn how to find the equation of a proportional relationship using a graph. In this problem, we use the formula y = mx to determine the equation of the line from given points. The example shows a linear graph passing through (0, 0) and (10, 5), with a slope of 1/2. Suitable 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