Question

Find the equation in standard form of the line with slope

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 7}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{7}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=\cfrac{7}{2}(x-5)\implies y-7=\cfrac{7}{2}x-\cfrac{35}{2} \\\\\\ y=\cfrac{7}{2}x-\cfrac{35}{2}+7\implies \stackrel{standard~form}{-\cfrac{7}{2}x+y=-\cfrac{21}{2}}$