The equation \( y = \frac{1}{5}x \) represents a linear function, and its graph is a straight line. Here are some characteristics of the graph:
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Slope: The slope of the line is \( \frac{1}{5} \). This means that for every 5 units you move to the right along the x-axis, the line will move up 1 unit on the y-axis. The line rises gradually.
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Y-Intercept: The y-intercept of the line is 0, which means the line crosses the y-axis at the point (0, 0).
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Direction: The line will pass through the origin (0, 0) and will rise as it moves to the right and fall as it moves to the left.
To sketch the graph:
- Start by plotting the y-intercept (0, 0).
- From (0, 0), move right 5 units along the x-axis and up 1 unit to reach the point (5, 1).
- Connect these points with a straight line that extends in both directions.
The resulting graph will be a straight line that extends infinitely in both directions through the origin, with a gentle upward slope.
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