Summary of "DIRECT VARIATION || GRADE 9 MATHEMATICS Q2"

Main Ideas and Concepts

Direct Variation Definition:
A Direct Variation occurs when two quantities have a constant ratio. This relationship can be expressed mathematically as y = kx, where k is the constant of variation.
Characteristics of Direct Variation:
If x increases, y also increases, and vice versa. The ratio y/x remains constant.
Mathematical Representation:
The equation y = kx can be used to describe the relationship between the two variables. The constant k can be calculated using k = y/x.
Applications of Direct Variation:
Examples include distance traveled over time, weight of an object in relation to its mass, and paycheck calculations based on hours worked.
Graphical Representation:
A graph of y against x for Direct Variation will show a straight line passing through the origin, indicating a linear relationship.

Identifying Direct Variation: Check if the ratio y/x is constant for given pairs of values.
Graphing: Use a Cartesian plane to plot points derived from the relationship y = kx.
Finding the Constant of Variation: Use the formula k = y/x with known values of y and x.
Writing Equations: Translate word problems into equations using the Direct Variation format y = kx.
Solving Problems: Substitute known values into the equation to find unknowns.

Bicycle Distance: Kyle's travel distance over time shows Direct Variation, with d = 10t.
Weight on Moon: The weight of an object on the moon varies directly with its weight on Earth, leading to the equation y = 0.16x.
Worker's Paycheck: The paycheck varies directly with hours worked, leading to calculations based on given hourly rates.