The linear function has the form y=mx+b, which I expect you have heard of. The 'b' is the y-intercept, and the 'm' is the slope.
A constant of proportionality is something you have with direct variation, which is where the line goes through (0,0). This happens when 'b' equals zero.
So now the equation is just y=mx, and the constant of proportionality is 'm'.
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The answer depends on what the constant is: the y-intercept in a linear graph, constant of proportionality, constant of integration, physical [universal] constant.
It will just be the gradient of the function, which should be constant in a linear function.
If the equation is y = kx then the constant of proportionality is k.
Yes.
x = constant.