Direct Proportion problems

Understanding Direct Proportion

Direct proportion is a relationship between two variables where if one variable is multiplied by a factor, the other variable is multiplied by the same factor.
This is often noted as ‘y is directly proportional to x’, which can be written as y ∝ x.
If y is directly proportional to x, you can write this as y = kx, where k is called the constant of proportionality.
You can find this constant k by rearranging the formula into k = y/x.

Solving Direct Proportion Problems

To solve a direct proportion problem, start by identifying which quantities are in direct proportion.
Find the scale factor or constant of proportionality, k.
Use this scale factor to find the unknown quantity by using the formula y = kx.

Example Problems

If y is directly proportional to x, and y = 15 when x = 5, we begin by finding the constant k. So, k = y/x = 15/5 = 3. Thus, the relationship can be written in the form y = 3x.
If a car travels at a constant speed, the distance it covers (d) is directly proportional to the time spent driving (t). If the car covers 60 miles in 2 hours, we can find the constant speed by k = d/t = 60/2 = 30 miles per hour. Hence, the proportional relationship is d = 30*t.

Remember, not all relationships are directly proportional. If you increase one variable and the other decreases, it’s called an inverse proportion. However, if one variable goes up and the other seems to go up and down randomly, it’s not directly or inversely proportional. It’s essential to identify the type of relationship correctly to solve any proportion problem.