A graph that represents a proportional relationship exhibits several key characteristics:
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Linear Relationship: The graph will be a straight line that passes through the origin (0,0). This is because a proportional relationship can be expressed in the form \(y = kx\), where \(k\) is a constant.
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Constant Ratio: The ratio of the y-value to the x-value will remain constant for any two points on the line. This means that as you double the x-value, the y-value will also double, maintaining the same ratio \(k\).
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Direct Variation: The relationship is one of direct variation, meaning that increases in one variable (x) will result in proportional increases in the other variable (y).
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No Intercept Other Than the Origin: The line will not intersect the y-axis at any point other than the origin, indicating that when x equals zero, y also equals zero.
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Symmetry: The graph is symmetric with respect to the origin, as a proportional relationship will behave similarly in all four quadrants of the coordinate plane.
In summary, a graph that is proportional will be a straight line through the origin with a constant slope, representing a consistent ratio between the two variables.