Question

i have two questions. Is y= (4 2/3) x proportonal? and is y= 3(x - 1) proportional? If it’s proportional, what’s the constant variable?

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y = 4\frac{2}{3}x\qquad \qquad yes\qquad \checkmark\qquad \qquad k = 4\frac{2}{3} \\\\[-0.35em] ~\dotfill\\\\ y=3(x-1)\implies \stackrel{\textit{distributing}}{y=3x-3}\qquad \qquad yes\qquad \checkmark \qquad \qquad k=3$

bear in mind that, direct proportional equations have a y-intercept.

for y = kx, is pretty much y = kx + 0, where 0 = y-intercept.

and the "k" constant of proportionality, is pretty much just its slope.