A graph of a slope of \( \frac{1}{3} \) represents a straight line that rises 1 unit on the vertical axis (y-axis) for every 3 units it moves horizontally on the horizontal axis (x-axis).
To illustrate this:
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Starting Point: You can start plotting the line from any point, but commonly it starts at the origin (0, 0).
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Plotting Points:
- From (0, 0), if you move 3 units to the right (to the point (3, 0)), you move up 1 unit (to the point (3, 1)).
- Similarly, if you start at (0, 0) and instead move 3 units to the left (to (-3, 0)), you would move down 1 unit to (-3, -1).
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Drawing the Line: You can draw a straight line through the points you have plotted (for instance, (0, 0), (3, 1), (-3, -1)).
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Equation: The equation of the line can be written in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For a slope of \( \frac{1}{3} \) that passes through the origin, the equation would be \( y = \frac{1}{3}x \).
The resulting line will tilt gently upwards from left to right due to the slope being positive but relatively small (1/3).
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