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?
If y varies directly with x, it means that y and x are directly proportional. This is represented by the equation y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = -252 when x = 84:
-252 = k * 84
Dividing both sides of the equation by 84:
k = -252/84
k = -3
Now that we have the value of k, we can substitute it into the equation y = kx to find y when x = 74:
y = -3 * 74
y = -222
Therefore, when x = 74, y = -222.
To find the value of y when x = 74, we can use the concept of direct variation. In a direct variation, y is directly proportional to x, which can be represented by the equation y = kx, where k is the constant of variation.
We can find the value of k by substituting the given values of y and x into the equation. So, when y = -252 and x = 84, we have:
-252 = k * 84
To isolate k, we divide both sides of the equation by 84:
k = -252 / 84 = -3
Now that we have the value of k, we can use it to find y when x = 74. Substituting the values into the equation y = kx:
y = -3 * 74
y = -222
Therefore, when x = 74, y is equal to -222.
To find the value of y for a given value of x when y varies directly with x, we can use the formula for direct variation: y = kx, where k is the constant of proportionality.
To find the value of k, we can use the given information that y = -252 when x = 84. Plugging these values into the formula, we have: -252 = k * 84.
Simplifying the equation, we divide both sides by 84: -252/84 = k. This gives us k = -3.
Now that we have the value of k, we can substitute it into the equation to find the value of y when x = 74: y = (-3)(74).
Evaluating the expression, we find y = -222.
Therefore, when x = 74, y is equal to -222.