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The answer to that will depend on what operator is supposed to be in place between the "1" and the "4y".

If it's 1 + 4y = 12 - 4x, then yes, that is linear. It would give you the line described by the equation y = 8/3 - x, which is a simple line with a slope of negative one, which intersects the axis at points (0, 8/3), and (8/3, 0).

If it's multiplication, 1 * 4y = 12 - 4x (or if that "1" is just a question number that you cut and pasted out of your homework), then this is also linear, also has a slope of -1, but intersects both axis at the point (0, 0).

If on the other hand, you mean 14y = 12 - 4x, then yes, that is also linear. This is because 1 to the power of anything is equal to one. That tells us that:
12 - 4x = 1
∴ -4x = -11
∴ x = 11/4
Which means that the equation describes a vertical line that passes through x-axis at (11/4, 0).

If you mean 1/4y = 12 - 4x, then no, this is not linear:
1/(4y) = 12 - 4x
∴4y = 1/(12 - 4x)
∴y = 1/(48 - 16x)
That would instead give you a curve where y approaches infinity as x approaches 0 and y approaches 0 as x approaches infinity.

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15y ago
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Q: Is 1 4y equals 12-4x a linear function?
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