I have recently been confused by the term "Proportional". This started when I came across 2 different websites that seem to contradict one another when it comes to $y = x^2$. The first implies that the two variables are proportional, but the second appears to deny this.
- Is Proportional link (mathisfun, near the bottom of webpage)
- Is NOT Proportional link (khan, near the end of the video)
I am sure that I am missing something and/or being overwhelmed by overloaded terms as both are reputable resources. The forms of proportional relationships that I am familiar with are the directly and indirectly proportional equations of $y = k * x$ and $y = k/x$ with '$k$' being a constant. So when I read that equations of the form $y = x^2$ (presumably w/ '$k$' $= 1$) being considered proportional, it throws me off. Also, the exponential form of $y= a * b^x$, where '$a$' is a constant, now has me rethinking its proportional nature . . . which to me has always just been based on the factor '$b$'. If one can say that "$y$ is proportional to $x^2$", then why can't one say "$y$ is proportional to $x+1$" (i.e. $y = 1 * (x + 1)$? I am clearly confused and would surely appreciate being set straight. Many thanks.