1. Suppose y varies directly with x and, y=15 and x=5. Write a direct variation equation that relates x and y. What is the value of y when x=9?
I need a little help on how to figure out how to write this out. Any help will be appreciated. Thank you
y=kx
so, y/x = k is constant.
You want y such that
y/9 = 15/5
You don't really need to know what k is.
Thank you for your help.
Well, well, well, it seems like we have some direct variation going on here! To write a direct variation equation, we'll use the form y = kx, where k is the constant of variation.
Now, we're given that y = 15 when x = 5. So, let's plug in those values and solve for k:
15 = k * 5
Now, let's isolate k by dividing both sides by 5:
k = 15/5
Simplifying that gives us:
k = 3
So, our direct variation equation is y = 3x.
Now, to find the value of y when x = 9, all we have to do is substitute x = 9 into the equation:
y = 3 * 9
And the punchline is...
y = 27!
To write a direct variation equation that relates x and y, we can use the formula:
y = kx
Where "k" is the constant of variation. In this problem, we have y = 15 when x = 5. We can use this information to find the value of k.
Substituting the given values into the equation:
15 = k * 5
To solve for k, divide both sides of the equation by 5:
k = 15/5 = 3
So, the direct variation equation that relates x and y is:
y = 3x
Now, to find the value of y when x = 9, we can substitute this value into the equation:
y = 3 * 9
Simplifying the equation, we have:
y = 27
Therefore, when x = 9, the value of y is 27.
To write a direct variation equation, you need to identify the constant of variation, which is the ratio of y to x. In other words, the equation will have the form y = kx, where k is the constant of variation.
Given that y varies directly with x, and y = 15 when x = 5, we can substitute these values into the direct variation equation to solve for k.
15 = k * 5
Now, divide both sides by 5 to isolate k:
k = 15 / 5
k = 3
Therefore, the direct variation equation that relates x and y is y = 3x.
To find the value of y when x = 9, we can substitute x = 9 into the direct variation equation:
y = 3 * 9
y = 27
So, when x = 9, y = 27.