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Assume that all variables represent real numbers. Determine whether the equation determines y to be a function of x.

A. y is a function of x.
B. y is not a function of x.

1 Answer

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Final answer:

The equations y = -3x, y = 0.2 + 0.74x, and y = -9.4 - 2x all define y as a function of x, as they are linear equations of the form y = mx + b, with m as the slope and b as the y-intercept.

Step-by-step explanation:

The question is asking us to determine whether an equation, given that all variables represent real numbers, defines y as a function of x. An equation determines y to be a function of x if for every value of x, there is exactly one corresponding value of y. Equations like y = mx + b, where m is the slope and b is the y-intercept, are linear and do define y as a function of x. This is because each value of x corresponds to exactly one value of y. Examples of linear equations given include y = -3x, y = 0.2 + 0.74x, and y = -9.4 - 2x. For these equations, they all have the form of y = mx + b, where m and b are constants, making them linear and confirming that in each of these cases, y is a function of x.

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