Question

Write an equation of the line that passes through the points (-3,4) and (-5,1)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 4}})\quad % (c,d) &({{ -5}}\quad ,&{{ 1}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-4}{-5-(-3)}\implies \cfrac{1-4}{-5+3} \\\\\\ \cfrac{-3}{-2}\implies \cfrac{3}{2}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{3}{2}[x-(-3)] \\\\\\ y-4=\cfrac{3}{2}(x+3)\implies y-4=\cfrac{3}{2}x+\cfrac{9}{2}\implies y=\cfrac{3}{2}x+\cfrac{9}{2}+4 \\\\\\ y=\cfrac{3}{2}x+\cfrac{17}{2}$