In a direct variation, y=
–
60 when x=5. Write a direct variation equation that shows the relationship between x and y.
The direct variation equation can be written as y = kx, where k is the constant of variation.
To find k, we can use the given information:
y = -60, x = 5
Substituting these values into the equation, we have:
-60 = 5k
Solving for k, we have:
k = -60/5 = -12
Therefore, the direct variation equation that shows the relationship between x and y is:
y = -12x
In a direct variation, the relationship between x and y 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.
When x = 5, y = -60.
Plugging in these values into the equation, we have: -60 = k * 5.
To solve for k, divide both sides of the equation by 5:
-60 / 5 = k.
Simplifying, we find that k = -12.
So the direct variation equation that shows the relationship between x and y is y = -12x.
To write a direct variation equation that shows the relationship between x and y, you need to determine the constant of variation, which represents the ratio between the two variables.
In this case, we are given that when x = 5, y = -60. To find the constant of variation, you divide y by x, using the given values:
Constant of Variation (k) = y / x
= -60 / 5
= -12
Now that we have the value of the constant of variation, we can write the direct variation equation:
y = kx
Plugging in the value of k, the equation becomes:
y = -12x
So, the direct variation equation that shows the relationship between x and y is y = -12x.