Often if you apply an affine transformation to a function f(x), you will not get back another function. For example, if you plot y=x^2, then rotate by 90 degrees, you will no longer have a function.

When you're dealing with straight lines, the worst thing you could encounter would be a vertical line. So this problem doesn't arise here.

If you want to work in more generality, you'll need to convert to a parametric equation. This might sound complicated at first (if you haven't encountered them before), but they're not that bad.

We could draw the parabola y=x^2 instead by plotting the points (t,t^2) where t runs from minus infinity to infinity (t is the parameter, hence the name "parametric equation"). So (t,t^2) is the same as y=x^2.

We can then multiply (t,t^2) by any affine transformation, for example, if we multiply it by

0 -1
1  0

then we obtain the parametric equation (t^2,-t). So we've rotated y=x^2 by 90 degrees.