Question

The graph shows the proportional relationship. Derive the equation of the line y = mx + b through the origin. * 1 point

y = 5x

y = x + 5

y = -5x

y = 5x + 5

Answer 1

In a proportional relationship represented by a graph that passes through the origin (0,0), the equation takes the form of \( y = mx \), where \( m \) is the slope of the line.

To derive the correct equation from the options provided, we can analyze each one:

1. **y = 5x**: This is in the form \( y = mx \) with a slope \( m = 5 \), passing through the origin.
2. **y = x + 5**: This has a y-intercept of 5, meaning it does not pass through the origin.
3. **y = -5x**: This is also in the form \( y = mx \) with a slope \( m = -5 \), passing through the origin.
4. **y = 5x + 5**: Similar to option 2, this has a y-intercept of 5, meaning it does not pass through the origin.

Since the question states the line must go through the origin, the valid options that meet this criterion are:

- \( y = 5x \)
- \( y = -5x \)

Without additional context about the graph (such as the steepness or direction of the line), we can't definitively choose one over the other. However, if the graph represents a positive proportional relationship (like a direct increase), then \( y = 5x \) is the correct answer.

If you are instructed to derive the equation based on a positive slope, the correct answer would be:

**y = 5x**