Input in standard form the equation of the given line. The line that passes through (1, 5) and (-2, 3)

Question 1

Input in standard form the equation of the given line.

The line that passes through (1, 5) and (-2, 3)

Question 2

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 5}})\quad % (c,d) &({{ -2}}\quad ,&{{ 3}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{3-5}{-2-1}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3}$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-5=\cfrac{2}{3}(x-1)\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-5=\cfrac{2}{3}x-\cfrac{2}{3}\implies -\cfrac{2}{3}x+y=5-\cfrac{2}{3}\implies \stackrel{\textit{standard form}}{-\cfrac{2}{3}x+y=\cfrac{13}{3}}$

Input in standard form the equation of the given line. The line that passes through (1, 5) and (-2, 3)

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