Question

Which equation represents a line that passes through (–2, 4) and has a slope of 2/5 ?

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{2}{5} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{2}{5}[x-(-2)] \implies y-4=\cfrac{2}{5}(x+2) \\\\\\ y-4=\cfrac{2}{5}x+\cfrac{4}{5}\implies y=\cfrac{2}{5}x+\cfrac{4}{5}+4\implies y=\cfrac{2}{5}x+\cfrac{24}{5}$