Question

graph the equation y=1/3x-2.
first identify the y-intercept
y-intercept__

Answer 1

To graph the equation \( y = \frac{1}{3}x - 2 \), we first identify the y-intercept. The y-intercept is the value of \( y \) when \( x = 0 \).

To find the y-intercept:

1. Set \( x = 0 \) in the equation:
\[
y = \frac{1}{3}(0) - 2 = -2
\]

So, the y-intercept is \(-2\).

### Next Steps to Graph:

1. **Plot the y-intercept**: Place a point at (0, -2) on the graph.

2. **Use the slope**: The slope of the equation is \( \frac{1}{3} \). This means that for every 3 units you move to the right (increase \( x \) by 3), you move up 1 unit (increase \( y \) by 1).

3. **Find another point**:
- Start at the y-intercept (0, -2).
- Move 3 units to the right (to \( x = 3 \)), then move up 1 unit (to \( y = -1 \)). This gives the point (3, -1).

4. **Plot the second point**: Place a point at (3, -1).

5. **Draw the line**: Connect the two points with a straight line, and extend the line in both directions.

The graph will show a straight line that crosses the y-axis at -2 and has a slope of \(\frac{1}{3}\).