Question

What equation represents a line that passes through (4,1/3) and has a slope of 3/4

Answer 1

$\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{\frac{1}{3}}) \qquad \qquad \qquad \qquad % slope = m slope = m\implies \cfrac{3}{4} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-\cfrac{1}{3}=\cfrac{3}{4}(x-4)\implies y-\cfrac{1}{3}=\cfrac{3}{4}x-3 \\\\\\ y=\cfrac{3}{4}x-3+\cfrac{1}{3}\implies y=\cfrac{3}{4}x-\cfrac{8}{3}$