Example Card: Identifying Direct Variation in an Equation
Identify direct variation relationships in equations in Grade 9 Algebra where y = kx. Verify direct variation by checking that the ratio y/x remains constant.
Key Concepts
An equation might not look like $y=kx$ at first, but a little algebra can reveal its true form. We will use the first key idea, Identifying Direct Variation from an Equation, to solve this problem.
Example Problem Tell whether the equation $y + 3x = 0$ represents a direct variation.
Step by Step 1. To determine if the equation represents a direct variation, we need to see if it can be written in the form $y = kx$. 2. Start with the given equation: $$y + 3x = 0$$ 3. To isolate $y$, we subtract $3x$ from both sides of the equation. $$y = 3x$$ 4. The equation is now in the form $y = kx$. This confirms it is a direct variation, and the constant of variation, $k$, is $ 3$.
Common Questions
How do you identify direct variation from an equation?
An equation shows direct variation if it can be written as y = kx where k is a nonzero constant and there is no added or subtracted constant. The line must pass through the origin for the relationship to be directly proportional.
What is the constant of variation k in a direct variation?
The constant k is the ratio y/x, which stays the same for every point in the relationship. Calculate k by dividing any y-value by its corresponding x-value. If the ratio is not constant, the equation is not a direct variation.
How does the graph of a direct variation equation look?
The graph is always a straight line passing through the origin (0, 0). The slope equals k, the constant of variation. A steeper line means a larger k value, while a flatter line means a smaller k.