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Find the value of y for a given value of x, if y varies directly with x.
If y = -252 when x = 84, what is y when x = 74?
To find the value of y when x = 74, we can set up a proportion using the direct variation equation.
The direct variation equation can be written as y = kx, where k is the constant of variation.
We can find the value of k by plugging in the values of y and x from the given information.
Given:
y = -252
x = 84
Plugging these values into the equation, we get:
-252 = k(84)
To solve for k, we divide both sides of the equation by 84:
k = -252/84
k = -3
Now that we have the value of k, we can use it to find the value of y when x = 74.
Plugging in the values of x and k into the direct variation equation, we get:
y = -3(74)
y = -222
Therefore, when x = 74, y is equal to -222.
To find the value of y when x = 74, we can use the direct variation formula:
y = kx
where y is the dependent variable, x is the independent variable, and k is the constant of variation.
To find the value of k, we can substitute the given values y = -252 and x = 84 into the formula:
-252 = k * 84
Next, we can solve for k by dividing both sides of the equation by 84:
k = -252 / 84
k = -3
Now that we know the value of k, we can use it to find the value of y when x = 74:
y = -3 * 74
y = -222
Therefore, when x = 74, y = -222.