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Yes.

A linear equation is one in which the maximum power of a variable (usually x) is 1.

In y = mx + b the x has a maximum power of 1.

If b = 0, the equation becomes y = mx and x still has a maximum power of 1.

The b is the y-intercept, ie it shifts the line up/down the y-axis and does not affect the shape of the graph, which stays a line: hence a linear equation.

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Q: Is y equals mx plus b linear equation when b equals 0?
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