Question

Write an equation of the line, in point-slope form, that passes through the two given points.

Answer 1

Slope is -10/20=-1/2

y-7=(-1/2)(x+15). answer C

Answer 2

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -15}} &,&{{ 7}}~) % (c,d) &&(~{{ 5}} &,&{{ -3}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-3-7}{5-(-15)}\implies \cfrac{-3-7}{5+15}$

$\bf \cfrac{-10}{20}\implies -\cfrac{1}{2} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-7=-\cfrac{1}{2}[x-(-15)] \\\\\\ y-7=-\cfrac{1}{2}(x+15)$