Direct and Inverse Proportion Graphs

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What is direct proportion?

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Direct proportion is a relationship between two variables where an increase in one variable results in a proportional increase in the other variable. This can be represented by the equation y = kx, where k is a constant.

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What is inverse proportion?

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Inverse proportion is a relationship between two variables where an increase in one variable results in a proportional decrease in the other variable. This can be represented by the equation y = k/x, where k is a constant.

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How can you identify a direct proportion graph?

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A direct proportion graph is a straight line that passes through the origin (0,0). The slope of the line represents the constant of proportionality.

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How can you identify an inverse proportion graph?

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An inverse proportion graph is a hyperbola that approaches the axes but never touches them. It shows that as one variable increases, the other decreases.

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What does it mean if a graph shows neither direct nor inverse proportion?

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If a graph shows neither direct nor inverse proportion, it means that the relationship between the two variables does not follow a consistent pattern of increase or decrease.

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What is the constant of proportionality in direct proportion?

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The constant of proportionality in direct proportion is the ratio of the two variables, often denoted as k in the equation y = kx.

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What is the constant of proportionality in inverse proportion?

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The constant of proportionality in inverse proportion is the product of the two variables, often denoted as k in the equation y = k/x.

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Can a graph represent both direct and inverse proportion?

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No, a graph cannot represent both direct and inverse proportion simultaneously. Each type of proportion has a distinct graphical representation.

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What is a real-world example of direct proportion?

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A real-world example of direct proportion is the relationship between distance and time when traveling at a constant speed.

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What is a real-world example of inverse proportion?

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A real-world example of inverse proportion is the relationship between the speed of a vehicle and the time taken to cover a fixed distance; as speed increases, time decreases.