Question

y=2/3x

Answer 1

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:

- If \( x = 0 \):
\[
y = \frac{2}{3}(0) = 0 \quad \text{(Point: (0,0))}
\]

- If \( x = 3 \):
\[
y = \frac{2}{3}(3) = 2 \quad \text{(Point: (3,2))}
\]

- If \( x = 6 \):
\[
y = \frac{2}{3}(6) = 4 \quad \text{(Point: (6,4))}
\]

- 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 \( y = \frac{2}{3}x \).