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Q: Explain how you can use a table of values and equation and a graph to determine whether a function represents a proportional relationship?

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If it passes through the origin

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The answer depends on what relationship - if any - exists between the points in the table. There need not be any relationship.

It is a straight line equation in the form of: y = mx+b whereas 'm' is the slope and 'b' is the y intercept

Directly proportional. From rearrangement of the equation D=M/V i.e. Volume by Density = Mass

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If it passes through the origin

You cannot represent a proportional relationship using an equation.

Time and power are inversely proportional to each other. This means that if power increases, time decreases, and vice versa. This relationship is expressed by the equation P = W/t, where P represents power, W represents work, and t represents time.

Boyle's Law states that the pressure of a gas is inversely proportional to its volume, when the temperature is held constant. Mathematically, this relationship is expressed as P1V1 = P2V2, where P represents pressure and V represents volume.

If you mean: y=7x -3 then it is a proportional relationship of a straight line equation.

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The graph of a linear proportion will be a straight line passing through the origin. The equation will have the form y = mx, also written as y = kx.

r = k(t^3 / s) where k is a constant of proportionality.

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For each of the following relationships, graph the proportional relationship between the two quantities, write the equation representing the relationship, and describe how the unit rate, or slope is represented on the graph.

Boyle's Law states that the pressure of a gas is inversely proportional to its volume, when the temperature is kept constant. This means that as the volume of a gas decreases, the pressure it exerts increases, and vice versa. This relationship is described by the equation P1V1 = P2V2, where P represents pressure and V represents volume.

Ohm's law is stated as V = I * R, where V represents voltage, I represents current, and R represents resistance. This equation describes the relationship between voltage, current, and resistance in an electrical circuit.