y varies directly as x
y=35 when x=10. Find the direct variation equation. Than find y when x=5
To find the direct variation equation, we need to determine the constant of variation. We can do this by using the given data: when x = 10, y = 35.
The equation for direct variation is in the form y = kx, where k is the constant of variation.
Plugging in the values y = 35 and x = 10 into the equation, we can solve for k:
35 = k(10)
Dividing both sides by 10, we find:
k = 35/10
k = 3.5
Therefore, the direct variation equation is y = 3.5x.
To find y when x = 5, we can plug this value into the equation:
y = 3.5(5)
y = 17.5
Therefore, when x = 5, y = 17.5.
To find the direct variation equation, we can use the given information that "y varies directly as x." This means that we can write the equation as:
y = kx
where k is the constant of variation.
Now, we can use the given data point (x = 10, y = 35) to find the value of k. Substituting these values into the equation, we have:
35 = k * 10
To solve for k, we divide both sides of the equation by 10:
k = 35/10
k = 3.5
So, the direct variation equation is:
y = 3.5x
Now, to find the value of y when x = 5, we can substitute x = 5 into the direct variation equation:
y = 3.5 * 5
y = 17.5
Therefore, when x = 5, y is equal to 17.5 in the direct variation equation.
To find the direct variation equation, we need to understand the concept of direct variation. In a direct variation, the ratio between the two variables remains constant. Mathematically, it can be expressed as y = kx, where k is the constant of variation.
Given that y varies directly as x, we can substitute the given values into the equation to find the value of k.
We are given that when x = 10, y = 35. Substituting these values into the equation, we get:
35 = k(10)
To solve for k, we divide both sides of the equation by 10:
35/10 = k
k = 3.5
So, the direct variation equation is y = 3.5x.
To find y when x = 5, we can substitute the value of x into the equation:
y = 3.5(5)
y = 17.5
Therefore, when x = 5, y = 17.5.