If y varies directly with x and y=30 when x=5, find y if x=-3
If “x” variation directly as yand x=5 and y=30 find the constant of variation and the equalation of variation
To find the value of y when x = -3, we need to use the concept of direct variation.
In a direct variation equation, y is directly proportional to x. This can be represented as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information:
When x = 5, y = 30.
Substituting these values into the equation, we get:
30 = k * 5
Now we can solve for k:
k = 30 / 5
k = 6
Now that we have the value of k, we can find the value of y when x = -3:
y = k * x
y = 6 * -3
y = -18
Therefore, when x = -3, y = -18.
To solve this problem, we need to utilize the concept of direct variation. Direct variation states that when two variables are directly proportional, their ratio remains constant.
Let's denote the constant of variation as k. In this case, since y varies directly with x, we can write the equation as:
y = kx
To find the value of k, we can use the given information that y = 30 when x = 5:
30 = k * 5
To solve for k, divide both sides of the equation by 5:
k = 30 / 5 = 6
Now that we know k, we can proceed to find the value of y when x = -3:
y = kx
y = 6 * (-3) = -18
Therefore, when x = -3, y will be equal to -18.
If y varies directly with x then:
y = k x
x = 5 , y = 30
30 = k ∙ 5
30 / 5 = k
6 = k
k = 6
y = 6 x
x = - 3
y = 6 x
y = 6 ∙ ( - 3 ) = - 18
OR
y / x = y / x
30 / 5 = y / ( - 3 )
6 = y / ( - 3 )
Multiply both sides by - 3
- 18 = y
y = - 18