which graph represents a function with direct variation
Types of Graphs
A function with direct variation has a linear relationship. A straight line that passes through the origin (0,0) represents this relationship. The equation for a function of this type is y = kx. If the slope is zero, the graph is a straight line. If the slope is positive, it is a quadratic function. Alternatively, a direct-variation function may be a cubic, quartic, or radical.
Direct and Inverse Variation Functions
A direct-variation function is the function whose value increases with time. If you want to graph it, you will plot a straight line through the origin. An inverse-variation function will have a curve that approaches the x-axis as x increases. Which graph does the function in question have? Which one represents a function with direct variation? How do you determine whether a graph represents a function?
Graph changes on the base of Conditions
If the value of a variable changes with time, the graph will show this variation. Y/x changes over time. In direct-variation, a graph shows the change in value as a function of x. The slope is k, and the curve is directly related to y. If the inverse-variation graph shows an increase in y, the graph of a variable equals x+k.
Straight Line Graph
A direct-variation graph passes through the origin. This graph is a straight line with a proportional relationship between x and y. The slope of the line is the k-value of the direct-variation function. Y is the value of k in the x-y equation, and x increases. The inverse-variation graph is a curve that moves away from the x-axis, and k is equal to x.
First Analyze the type of Variation
In a graph analysis problem, the goal is to determine whether the graph represents a function with direct variation or an inverse-variation. A direct-variation graph will be a straight line that passes through the origin, whereas an inverse-variation will have a curve that approaches the x-axis as x increases. This is not an easy problem to solve. Therefore, you must first understand how to analyze a direct-variation graph.
Examples
The graph of a function with direct variation is a straight line that passes through the origin. It will have a constant value of k, and the x-axis will be an arbitrary point. Inverse-variation graphs are the inverse of a direct-variation graph. This is not a graph that is a straight line. For example, a curve with the slope of x+k would be a line that passes through the origin.
Conclusion
A graph representing a function with direct variation is a straight line that passes through the origin. Inverse-variation graphs are slanted downward from left to right. By dividing x and y values, you can determine which is the correct graph to represent a function with direct variation. These diagrams may be difficult to interpret. If you don’t understand them, you can read the equation and the data in the paper.
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