If you know that a relationship is proportional and are given one ordered pair that is not (0,0), how can you find another pair?
THANK YOU!
just multiply both elements by the same nonzero value. Think of fractions.
To find another ordered pair in a proportional relationship, you can use the concept of ratios. In a proportional relationship, the ratio between the corresponding values of x and y remains constant.
Let's say we are given one ordered pair (x1, y1) that is not (0,0) in a proportional relationship. To find another pair, we need to determine the constant of proportionality (k) using the given pair.
Here's how you can find the constant of proportionality (k) and use it to find another pair:
1. Calculate the ratio (y1 / x1) using the given ordered pair.
2. Since the relationship is proportional, this ratio will be the same for all other pairs.
3. Let's call the unknown value of x in the new pair x2. Using the calculated ratio, set up the equation: y2 / x2 = y1 / x1.
4. Rearrange the equation to solve for y2: y2 = (y1 * x2) / x1.
5. Plug in different values for x2 to calculate the corresponding values of y2, creating multiple ordered pairs.
For example, let's say we have a proportional relationship with the given pair (3, 6). To find another pair, we calculate the ratio (y1 / x1) = (6 / 3) = 2.
Now, for different values of x2:
- When x2 = 4, y2 = (6 * 4) / 3 = 8.
- When x2 = 5, y2 = (6 * 5) / 3 = 10.
- When x2 = 6, y2 = (6 * 6) / 3 = 12.
So, the new pairs could be (4, 8), (5, 10), and (6, 12), all of which maintain the proportional relationship with the given pair (3, 6).
Remember, this method works for any given ordered pair in a proportional relationship (excluding the origin point (0,0)), and you can find multiple pairs using different values for x2.