Question

if a graph is proportional what characteristics will it display

Answer 1

A graph that represents a proportional relationship exhibits several key characteristics:

1. **Linear Relationship**: The graph will be a straight line that passes through the origin (0,0). This is because a proportional relationship can be expressed in the form \(y = kx\), where \(k\) is a constant.

2. **Constant Ratio**: The ratio of the y-value to the x-value will remain constant for any two points on the line. This means that as you double the x-value, the y-value will also double, maintaining the same ratio \(k\).

3. **Direct Variation**: The relationship is one of direct variation, meaning that increases in one variable (x) will result in proportional increases in the other variable (y).

4. **No Intercept Other Than the Origin**: The line will not intersect the y-axis at any point other than the origin, indicating that when x equals zero, y also equals zero.

5. **Symmetry**: The graph is symmetric with respect to the origin, as a proportional relationship will behave similarly in all four quadrants of the coordinate plane.

In summary, a graph that is proportional will be a straight line through the origin with a constant slope, representing a consistent ratio between the two variables.