Algebraic and graphical representations of direct proportion

What is direct proportion?

Direct proportion is a relationship between two variables where one is a constant multiple of the other. If y is directly proportional to x, then y = kx, where k is the constant of proportionality.

How is direct proportion represented algebraically?

Algebraically, direct proportion is represented by the equation y = kx, where y and x are the variables and k is the constant of proportionality. This equation shows a linear relationship passing through the origin.

How is direct proportion represented graphically?

Graphically, direct proportion is represented by a straight line that passes through the origin (0,0). The slope of the line is equal to the constant of proportionality, k. A steeper line indicates a larger value of k, showing a stronger direct proportion.

What does the constant of proportionality indicate?

The constant of proportionality, k, indicates the ratio between the two variables in direct proportion. It tells you how much y changes for each unit change in x. If k is large, a small change in x results in a large change in y, and vice versa.

Examples of direct proportion?

1. The cost of buying apples: The total cost is directly proportional to the number of apples bought if each apple costs the same.
2. Distance and time at constant speed: The distance traveled is directly proportional to the time spent traveling if the speed is constant, represented as d = vt, where v is the constant speed.