DIRECT VARIATION || GRADE 9 MATHEMATICS Q2

The video introduces direct variation, outlining objectives such as illustrating situations involving it, translating statements into mathematical equations, and solving related problems. Direct variation occurs when the ratio between pairs of numbers is constant, expressed as y = kx, where k is the constant of variation or proportionality.

An example demonstrates direct variation using Kyle's bicycle travel. A table shows distance (d) increasing directly with time (t). The constant of variation (k) is found to be 10 (d/t = 10). The graph of d against t is a straight line, and the equation is d = 10t. This equation is then used to predict distances for different times.

The video provides examples of translating verbal statements into direct variation equations. Examples include 'the fare (f) of a passenger varies directly as the distance (d)' becomes f = kd, and 'the weight (w) of an object is directly proportional to its mass (m)' becomes w = km.

Several examples illustrate how to find the constant of variation (k) and the equation of variation. Given y varies directly as x, and specific values for y and x, 'k' is calculated (e.g., if y=24 when x=6, then k=4). This 'k' is then used to form the equation of variation (e.g., y = 4x).

The video demonstrates solving problems where one variable's value needs to be found given a new value of the other variable, after determining the constant of variation and equation. This includes examples using both given conditions and data from a table of values.

Two word problems illustrate direct variation in real-world scenarios. One involves a worker's paycheck varying directly with hours worked, and another relates an object's weight on the moon directly to its weight on Earth. Both examples follow the steps of translating the problem, finding the constant, and using the equation to answer the question.

A short quiz with five multiple-choice questions tests the viewer's understanding of direct variation concepts, including identifying correct statements, finding the constant of variation, determining the equation of variation, and recognizing examples of direct variation.