the value of y varies directly with x, and y= -14 when x = 1/2. find y when x = -1.
two ways to do this:
1.
"y varies directly with x " y = kx , where k is a constant
when x = 1/2, y = -14
-14= (1/2)k
k = -28
so y = -28x
if x = -1
y = -28(-1) = 28
2. Just use a ratio:
(1/2) / -14 = -1/y
1/2)y = 14
y = 28
notice the actual "calculation " is the same
To find the value of y when x = -1, we can use the concept of direct variation.
The equation for direct variation is y = kx, where k represents the constant of variation.
To find the value of k, we substitute the given values for y and x into the equation and solve for k.
y = kx
-14 = k(1/2)
Solving for k:
-14 = k/2
k = -28
Now that we have the value of k, we can substitute x = -1 into the equation to find y:
y = kx
y = -28(-1)
y = 28
Therefore, when x = -1, y = 28.
To find the value of y when x = -1, we need to use the given information that "the value of y varies directly with x."
When two variables vary directly, their relationship can be represented by an equation of the form y = kx, where k is a constant.
In this case, we are given that y = -14 when x = 1/2. We can use this information to find the value of k.
Substitute the given values into the equation: -14 = k(1/2).
To solve for k, we can multiply both sides of the equation by 2 to eliminate the fraction: -14 * 2 = k(1/2) * 2.
Simplifying, we have -28 = k.
Now that we know the value of k, we can use it to find y when x = -1.
Plug in the values of x and k into the equation: y = kx.
Substituting x = -1 and k = -28, we get y = -28 * -1.
Simplifying, y = 28.
Therefore, when x = -1, y = 28.