how do you read graphs showing direct variation and inverse variation??
To read graphs showing direct variation and inverse variation, follow these steps:
Direct Variation:
1. Direct variation is represented by a linear graph that passes through the origin (0,0). This means that as one variable increases, the other variable also increases in a proportional manner.
2. Look for a straight line that doesn't intersect the x-axis or y-axis at any other point except the origin. The slope of the line represents the constant of variation.
3. To determine the relationship between the variables, observe how the line is slanted. If the line is slanted upwards from left to right, it indicates a positive direct variation. If it is slanted downwards, it indicates a negative direct variation.
Inverse Variation:
1. Inverse variation is represented by a hyperbolic graph. This means that as one variable increases, the other variable decreases, and vice versa.
2. Look for a curve that is symmetrical about the y-axis (vertical axis) or x-axis (horizontal axis), resembling an upside-down "U" or "∩" shape.
3. Note that the closer the values are to zero, the steeper the curve becomes, indicating a stronger inverse variation. The general equation for inverse variation is y = k/x, where "k" represents the constant of variation.
Remember, these guidelines are helpful to read and interpret graphs showing direct variation and inverse variation.