Suppose y varies directly with x. If y = 6 when x = −2, find x when y is 9.
The simplest to approach this problem would be to find the distance between the first x and y values.
6-(-2)=?
Use the number found and subtract it from your second y value "9"
9-?=??
You subtract because the x value is less than the y value as shown in the relationship between the first x & y values
To solve this problem, we need to understand what it means for two variables to be directly proportional. When two variables, let's say y and x, are directly proportional, it means that as one variable increases, the other variable also increases proportionally. In mathematical terms, we can express this relationship as y = kx, where k is the constant of proportionality.
Given that y varies directly with x, we can use the given information to find the constant of proportionality (k). The problem states that y is equal to 6 when x is equal to -2. Substituting these values into the equation, we have:
6 = k(-2)
To solve for k, divide both sides of the equation by -2:
6 / -2 = k
Simplifying this expression, we get k = -3.
Now that we know the constant of proportionality, we can use it to find x when y is 9. We'll use the same equation but rearrange it to solve for x:
y = kx
Substituting the given value of y (9) and the value of k (-3):
9 = -3x
To solve for x, divide both sides of the equation by -3:
9 / -3 = x
Simplifying this expression, we get x = -3.
Therefore, when y is 9, x is -3.