Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the value of y for a given value of x, if y varies directly with x.
If y = −252 when x = 63, what is y when x = 74?
If y varies directly with x, this means that we can write an equation in the form y = kx, where k is the constant of variation.
To find the value of k, we can use the given information. We are told that when x = 63, y = -252. Plugging these values into the equation, we get:
-252 = k(63)
To solve for k, divide both sides of the equation by 63:
k = -252/63 = -4
Now that we know the value of k, we can use it to find the value of y when x = 74. Plugging the values into the equation y = kx:
y = -4(74)
y = -296
Therefore, when x = 74, y = -296.
To find the value of y when x = 74, we can use the concept of direct variation.
In direct variation, we have the equation y = kx, where k is the constant of variation.
To find the value of k, we can use the given information: when x = 63, y = -252.
Substituting these values into the equation, we get:
-252 = k * 63
To find the value of k, divide both sides of the equation by 63:
k = -252 / 63
k = -4
Now that we have the value of k, we can use it to find the value of y when x = 74.
Substituting x = 74 and k = -4 into the equation y = kx, we get:
y = -4 * 74
y = -296
Therefore, when x = 74, y = -296.
To find the value of y when x = 74, we can use the concept of direct variation.
In direct variation, y varies directly with x, which means that y and x are proportional to each other. This can be 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. We know that when x = 63, y = -252. Plugging these values into the equation, we get:
-252 = k * 63
Now we can solve for k:
k = -252/63
k = -4
Now that we have the value of k, we can use it to find the value of y when x = 74. Plugging this value into the equation:
y = k * x
y = -4 * 74
y = -296
Therefore, when x = 74, y = -296.