The equation \( y = \frac{2}{3}x \) represents a linear function where \( y \) is directly proportional to \( x \).
Here’s a breakdown of the components:
- Slope: The coefficient \(\frac{2}{3}\) is the slope of the line. This means that for every 3 units increase in \( x \), \( y \) increases by 2 units.
- Y-intercept: Since there is no constant added (the equation is in the form of \( y = mx + b \), where \( b = 0\)), the y-intercept is at \( (0,0) \).
Characteristics
- The line passes through the origin (0, 0).
- It rises as \( x \) increases, indicating a positive correlation.
Example Points on the Line
To better understand this line, you can calculate a few points:
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If \( x = 0 \): \[ y = \frac{2}{3}(0) = 0 \quad \text{(Point: (0,0))} \]
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If \( x = 3 \): \[ y = \frac{2}{3}(3) = 2 \quad \text{(Point: (3,2))} \]
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If \( x = 6 \): \[ y = \frac{2}{3}(6) = 4 \quad \text{(Point: (6,4))} \]
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If \( x = -3 \): \[ y = \frac{2}{3}(-3) = -2 \quad \text{(Point: (-3,-2))} \]
You can plot these points on a coordinate plane to visualize the line represented by the equation \( y = \frac{2}{3}x \).