Each ordered pair is a solution of a direct variation. Write the equation of direct variation.
(2,10)
(8,2)
(7,21)
(2,-16)
Please Help!
A direct variation is such that the ratio of y/x is always constant (but x≠0).
For example, the line
L: y=2x is a direct variation.
Points on the line could be (1,2),(2,4),(5,10), noting that the ratio x/y is always 1/2. Consequently, the line passes through origin.
The general equation of a direct variation is y=mx.
Given an ordered pair where x≠0 and y≠0, we can find m by substituting x and y into the general equation.
For example, for the point (2,10), we put 10=m(2), solving gives m=10/2=5.
The equation of the direct variation is therefore:
y=5x
I will leave the rest to you as an exercise.
(x,8) and (6,-16) can you give me the answer that's all I need thanks
To write the equation of a direct variation, we need to find the constant of variation (k) and use it to form the equation y = kx.
Let's find the constant of variation for each pair:
1) (2,10):
We can see that as x increases from 2 to 8, y decreases from 10 to 2. This indicates an inverse relationship. Direct variations have a positive relationship, so this pair does not represent a direct variation.
2) (8,2):
Again, as x increases from 8 to 2, y decreases from 2 to -16. This also indicates an inverse relationship, so this pair does not represent a direct variation either.
3) (7,21):
Here, as x increases from 7 to 2, y increases from 21 to -16. This indicates an inverse relationship, not a direct variation.
4) (2,-16):
Now, as x remains constant at 2, y decreases from -16 to -16. This indicates a constant value of y, which is a direct variation.
Therefore, only the pair (2,-16) represents a direct variation. Thus, the equation of direct variation can be written as y = kx.
To write the equation of direct variation, we need to determine the constant of variation, also known as the k-value.
The equation of direct variation is in the form y = kx, where x represents the independent variable and y represents the dependent variable.
Let's take the first set of ordered pairs (2,10) to find the k-value:
10 = k * 2
To solve for k, we divide both sides of the equation by 2:
k = 10/2
k = 5
Now, we have the value of k as 5. Therefore, the equation of direct variation is:
y = 5x
We can verify this equation with the other sets of ordered pairs:
For (8, 2):
2 = 5 * 8
2 = 40 (Not a correct equation)
For (7, 21):
21 = 5 * 7
21 = 35 (Not a correct equation)
For (2, -16):
-16 = 5 * 2
-16 = 10 (Not a correct equation)
Therefore, the equation of direct variation based on the given ordered pairs is y = 5x.