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:
- Set \( x = 0 \) in the equation: \[ y = \frac{1}{3}(0) - 2 = -2 \]
So, the y-intercept is \(-2\).
Next Steps to Graph:
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Plot the y-intercept: Place a point at (0, -2) on the graph.
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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).
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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).
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Plot the second point: Place a point at (3, -1).
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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 \(\frac{1}{3}\).
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