https://file.aiquickdraw.com/mathbot/file/1725486181485qwnh5e0b.jpg

The graph you uploaded shows a straight line passing through the origin, which indicates a proportional relationship between \(x\) and \(y\). To find the equation of this line, we need to determine the slope, \(m\), of the line, and then write the equation in the form:

\[
y = mx
\]

### Finding the Slope:
To calculate the slope, we use two points on the line. From the graph, the line passes through the origin \((0,0)\) and another point, \((5, 10)\).

The slope formula is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((0,0)\) and \((5,10)\):

\[
m = \frac{10 - 0}{5 - 0} = \frac{10}{5} = 2
\]

### Equation of the Line:
Since the slope is \(2\), the equation representing the proportional relationship is:

\[
y = 2x
\]

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How do you determine the slope when the line does not pass through the origin?
2. What does it mean for a relationship to be "proportional"?
3. How would the graph change if the slope were negative?
4. What is the effect of changing the slope on the steepness of the line?
5. How would you represent a horizontal line on a graph?

**Tip**: In a proportional relationship, the ratio of \(y\) to \(x\) is constant, which is why the line passes through the origin.

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

Learn how to determine the equation of a line representing a proportional relationship using slope and points on a graph. This problem illustrates how to find the slope and use it to write the equation of a line, suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation