Table of Contents
How do you know if a variation is direct?
Direct and Inverse Variation. Two variables vary directly if there is a nonzero number for which the following is correct: In this equation, x and y are the two variables and k is the nonzero number, known as the constant of variation. The graph of y = kx is a line through the origin, and the slope of said graph is k.
Which is an example of a direct variation?
For example, if y varies directly as x, and y = 6 when x = 2, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
Is Y 4x direct proportion?
1 Expert Answer So y = 4x would be a direct variation (k=4), but not y = 4x+1.
Is Y 15x a direct variation?
Yes, the equation y=−15x is a direct variation, and -15 is the constant of variation. In order to be a direct variation, the line must go through the origin (0,0), which this equation does. Also, the slope is the constant of variation.
How do you know if a variation is direct or inverse?
For direct variation, use the equation y = kx, where k is the constant of proportionality. For inverse variation, use the equation y = k/x, again, with k as the constant of proportionality.
What equation represents a direct variation?
The general equation for direct variation is the linear equation, y = kx where k is the constant of variation (or constant of proportion).
Is xy 10 a direct variation?
y=x10 is a direct variation, because everything you do to y will result in a similar change in x .
Is Y 3 4x a direct variation?
Since the equation can be written in the form y=kx y = k x , y varies directly with x and k . The constant of variation, k , is 34 .
When do you Say Y varies directly with X?
We say y varies directly with x (or as x , in some textbooks) if: y = k x. for some constant k , called the constant of variation or constant of proportionality . (Some textbooks describe direct variation by saying ” y varies directly as x “, ” y varies proportionally as x “, or ” y is directly proportional to x .”)
When to use direct variation in a relationship?
Direct variation describes a simple relationship between two variables . We say y varies directly with x (or as x , in some textbooks) if: y = k x. for some constant k , called the constant of variation or constant of proportionality .
How to write the graph of the direct variation equation?
The graph of the direct variation equation is a straight line through the origin. Given that y varies directly as x , with a constant of variation k = 1 3 , find y when x = 12 . Write the direct variation equation. Substitute the given x value.
How is the ratio of Y and X always the same?
This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same. The graph of the direct variation equation is a straight line through the origin. Given that y varies directly as x , with a constant of variation k = 1 3 , find y when x = 12 .