The value of y varies directly with x. If x=10, then y=6
What is the value of x when y=9?
To find the value of x when y=9, we can set up a proportion using the direct variation relationship.
Since the value of y varies directly with x, we can write the proportion as:
y/x = k
where k is the constant of variation.
Using the given information, we can substitute the values:
6/10 = k
To find k, divide 6 by 10:
k = 6/10 = 0.6
Now we can use the proportion to find x when y=9:
9/x = k
Substitute the value of k:
9/x = 0.6
To find x, cross-multiply:
9 = 0.6x
Divide both sides by 0.6:
9/0.6 = x
Simplifying the right side:
15 = x
Therefore, when y=9, x=15.
To find the value of x when y=9, we can use the concept of direct variation.
Direct variation can be represented using the equation y = kx, where k is the constant of variation.
Given that when x=10, y=6, we can substitute these values into our equation:
6 = k(10)
To solve for k, we divide both sides of the equation by 10:
6/10 = k
Simplifying, we get:
3/5 = k
Now that we have the value of k, we can substitute it back into the equation and solve for x when y=9:
9 = (3/5)x
To isolate x, we can multiply both sides of the equation by 5/3:
9 * (5/3) = x
Simplifying, we get:
15 = x
Therefore, when y=9, the value of x is 15.
To find the value of x when y = 9, we can use the given information that y varies directly with x. This means that there is a constant of variation (k) that relates the two variables.
In this case, if x = 10, then y = 6. We can use this information to find the constant of variation (k).
To find k, we can use the formula for direct variation:
y = kx
Plugging in the given values, we have:
6 = 10k
Solving for k, we divide both sides by 10:
k = 6/10
k = 0.6
Now that we know the constant of variation, we can find the value of x when y = 9 by rearranging the equation:
y = kx
Plugging in the values, we have:
9 = 0.6x
We can solve for x by dividing both sides by 0.6:
x = 9/0.6
x = 15
Therefore, when y = 9, the value of x is 15.