Which Graph Represents a Function with Direct Variation?
In mathematics, direct variation is a relationship between two variables in which one variable is a constant multiple of the other. In other words, if two variables are in direct variation, then as the value of one variable increases, the value of the other variable increases by the same factor.
The graph of a function with direct variation is a straight line that passes through the origin. This is because the constant of variation, which is the slope of the line, is nonzero.
Questions:
- Which graph represents a function with direct variation?
The answer is the graph that passes through the origin and has a nonzero slope.
Explanation:
A graph represents a function with direct variation if it passes through the origin and has a nonzero slope. The origin is the point (0, 0), and the slope of a line is calculated by finding the rise over run.
The rise is the difference in the y-coordinates of two points on the line, and the run is the difference in the x-coordinates of the same two points. If the slope is nonzero, then the line has a constant rate of change.
In the graph below, the green line passes through the origin and has a nonzero slope. Therefore, the green line represents a function with direct variation.
[Image of a graph with a green line passing through the origin]The red line does not pass through the origin, so it does not represent a function with direct variation. The blue line has a slope of 0, so it also does not represent a function with direct variation.
Examples of direct variation:
- The area of a rectangle is directly proportional to its length and width.
- The distance traveled by a car is directly proportional to the time it travels at a constant speed.
- The current through a wire is directly proportional to the voltage applied to the wire.
In each of these examples, the two variables are related in such a way that as the value of one variable increases, the value of the other variable increases by the same factor.
