The ordered pairs in each exersise are for the same direct variation. Find each missing value.
(-2,8) and (x,12)
(4,y) and ( 16,12)
-3 and +3
For each, the y/x ratio remains constant
To find each missing value in the given exercises, we can use the concept of direct variation. In a direct variation, the ratio between the two variables remains constant. This means that if we have two ordered pairs representing a direct variation, we can find the missing values by setting up ratios and solving for the unknowns.
Exercise 1:
The given ordered pairs are (-2,8) and (x,12). To find the missing value, we need to determine the ratio between the x-values and the y-values.
The ratio for direct variation is: x1 / y1 = x2 / y2
Substituting the given values, we get: -2 / 8 = x / 12
Now, let's solve for x by cross-multiplying and simplifying the equation:
-2 * 12 = 8 * x
-24 = 8x
x = -24 / 8
x = -3
Therefore, the missing value in the first exercise is x = -3.
Exercise 2:
The given ordered pairs are (4,y) and (16,12). Let's set up the ratio using the same method as above:
The ratio is: x1 / y1 = x2 / y2
Substituting the given values, we get: 4 / y = 16 / 12
Now, let's solve for y by cross-multiplying and simplifying the equation:
4 * 12 = 16 * y
48 = 16y
y = 48 / 16
y = 3
Therefore, the missing value in the second exercise is y = 3.
So, the missing values for the given exercises are x = -3 and y = 3, respectively.