Question

How do you know if a straight line on a graph represents a proportional relationship?

Answer 1

Answer :If the graph is not a straight line, it does not represent a proportional relationship and also If the graph does not go through the origin, it does not represent a proportional relationship. If it is a line or ray that goes through the origin it is proportional and has a proportional relationship.

Answer 2

A straight line on a graph represents a proportional relationship if and only if it passes through the origin and has a constant slope.

Explanation:

A straight line on a graph represents a proportional relationship if and only if the line passes through the origin and has a constant slope. This means that the ratio of y to x (y/x) is the same for all points on the line.

`\textsf{For example:}`

The graph of y = kx, where k is a constant, is a straight line that passes through the origin and has a constant slope of k.

This means that the relationship between y and x is proportional, and the value of y is always k times the value of x.

The key characteristics of a proportional relationship represented by a straight line on a graph are:

• Straight Line: The graph will be a straight line.
• Passing through Origin: The line will pass through the origin (0,0).
• Constant Ratio: The ratio of y to x (y/x) is a constant value for all points on the line.

If a straight line on a graph does not pass through the origin or does not have a constant slope, then it does not represent a proportional relationship.