Hi. Please, explain the solution to this question:

If the slope of a linear equation f(x) is 2 and the y intercept is -2, then what is the y intercept of 3f(x-2)-3

If you know the slope and the y-intercept, then you know all you need to put the f(x) into slope-intercept form (ymxb, where m is the slope and b is the y-intercept). In this case, you have f(x)=2x-2.

To go from there to 3f(x-2)-3, your first step should be to get the f(x-2) out of there. To do that, just put in x-2 everywhere the original function has x:

If f(x)=2x-2, then f(x-2)=2(x-2)-2, which simplifies to f(x-2)=2x-6.

Once you’ve got that, substitute and simplify:


That’s in mxb form, so the y-intercept is –21.



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