How to identify inverse and direct variation . Can you explain with an example?
Answers
Answer:
"PLEASE MARK BRAINLIST"
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
Step-by-step explanation:
If the variables x and y vary directly when x = 3 and y = 15, then:
a. Write an equation that relates x and y.
b. Find the value of y when x = 6.
Solution
a. Because x and y vary directly, the equation is in the form y = kx. We can then solve for k by using the given values for x and y.
The equation that relates x and y is y = 5x.
b. To find the value of y, we substitute for x.
Then when x = 6, y =30.
Using a Ratio to Model Direct Variation
The direct variation model can be rewritten in ratio form
The ratio form lets you know that when x and y have direct variation, the ratio of x to y is alike for all values of x and y. Occasionally, real-life figures can be approximated by a direct variation model, although the data might not fit the model exactly.
Answer:
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. Remember that these problems might use the word 'proportion' instead of 'variation,' but it means the same thing.
example-Direct Variation: Because k is positive, y increases as x increases. So as x increases by 1, y increases by 1.5.
Inverse Variation: Because k is positive, y decreases as x increases.