Question

What is the equation for passing through (-2,2) and (5,3)

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -2}} &,&{{ 2}}~) % (c,d) &&(~{{ 5}} &,&{{ 3}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{3-2}{5-(-2)}\implies \cfrac{3-2}{5+2}\implies \cfrac{1}{7}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=\cfrac{1}{7}[x-(-2)] \implies y-2=\cfrac{1}{7}(x+2) \\\\\\ y-2=\cfrac{1}{7}x+\cfrac{2}{7}\implies y=\cfrac{1}{7}x+\cfrac{2}{7}+2\implies y=\cfrac{1}{7}x+\cfrac{16}{7}$