Question

an electrition charged $70 for 2 hours of work and 115 for 5hours of work write an equtionto find the cost for y and xk

Answer 1

$\bf \begin{array}{ccll} \stackrel{x}{hours}&\stackrel{y}{cost}\\ \cline{1-2} 2&70\\ 5&115 \end{array}~\hspace{10em}(\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{115}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{115-70}{5-2}\implies \cfrac{45}{3}\implies 15$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-70=15(x-2)\implies y-70=15x-30 \\\\\\ y=15x+40\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

as you already know, a direct proportional variation has a constant of variation "k", y = kx, which in this case that'd be the slope, namely 15.