how do you read graphs showing direct variation and inverse variation??
To read graphs showing direct variation and inverse variation, follow these steps:
1. Understand direct variation: In a direct variation, when one variable increases, the other variable also increases, and vice versa. It can be represented by the equation y = kx, where k is the constant of variation.
2. Examine the graph of direct variation: On a graph showing direct variation, the points will lie on a straight line passing through the origin (0,0). The slope of this line represents the constant of variation, k. If the line is steep, it means the variables change rapidly, while a less steep line indicates a slower change.
3. Interpret the slope: The slope of the line in a direct variation graph indicates the rate at which one variable changes with respect to the other. For example, if the slope is 2, it means for every unit increase in x, y increases by 2 units.
4. Understand inverse variation: In an inverse variation, when one variable increases, the other variable decreases, and vice versa. It can be represented by the equation y = k/x, where k is the constant of variation.
5. Examine the graph of inverse variation: On a graph showing inverse variation, the points will lie on a curve that is not a straight line. The curve will have a hyperbolic shape, and it will not intersect the x or y axis. The closer the points on the graph are to the axes, the more significant the variation.
6. Interpret the shape of the curve: The shape of the curve in an inverse variation graph shows the relationship between the variables. If the curve approaches the x-axis but never touches it, it indicates that as x gets larger, y gets closer to 0, but they are never equal. Similarly, if the curve approaches the y-axis but never touches it, it shows that as y gets larger, x gets closer to 0, but they are never equal.
By understanding the concepts of direct variation and inverse variation, as well as interpreting the graphs, you can effectively read and understand the relationship between variables.