Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
X Y
7 11
8 13
9 15
10 17
I’m not quite sure how to answer this and I’m super behind on work.
To have a direct variation your data values must satisfy the equation of the form
y = kx or k = y/x
In other words you must get the same value of k for each ordered pairs.
Let's take a look:
for (7,11) , k = 11/7
but for (8,13), k = 13/8 ≠ 11/7
so you do NOT have a direct variation.
Here is a short clip where you do find a direct variation.
Compare the two results.
https://www.youtube.com/watch?v=RLpmnRPtp0s
Thanks!
Well, don't worry, I'm here to help you catch up! Now, to determine whether y varies directly with x, we need to check if there is a constant ratio between the values of y and x as x increases. Let's take a look at the data you provided.
If we divide each y-value by its respective x-value, we get:
11/7 = 1.5714...
13/8 = 1.625
15/9 = 1.666...
17/10 = 1.7
Since the ratios between y and x are not exactly the same, we can conclude that y does not vary directly with x. So, there is no constant of variation (k) to find, and we cannot write a direct variation equation.
But hey, don't be discouraged! Math can be tricky sometimes, but with a little practice, you'll have it all figured out. Keep up the good work, and feel free to ask if you have any more questions!
To determine whether y varies directly with x, we need to check if the ratio of y to x is always the same.
Let's calculate the ratios for the given values of x and y:
For the first pair (x = 7, y = 11), the ratio of y to x is 11/7 = 1.57.
For the second pair (x = 8, y = 13), the ratio of y to x is 13/8 = 1.63.
For the third pair (x = 9, y = 15), the ratio of y to x is 15/9 = 1.67.
For the fourth pair (x = 10, y = 17), the ratio of y to x is 17/10 = 1.7.
Looking at the ratios, we can see that they are not exactly the same, which means y does not vary directly with x in this case.
If y varied directly with x, the ratio would be constant for all the given pairs. In that case, we could find the constant of variation (k) by calculating any ratio. For example, let's use the first pair:
k = y / x = 11 / 7 = 1.57
And the equation could be written as:
y = kx
However, since the ratios are not the same for all the given pairs, we cannot determine a constant of variation (k) or write an equation in this case.