Question

What is -2/5 as y=mx=b form or into slope intercept form

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ -5}} &,&{{ -1}}~) % (c,d) &&(~{{ 5}} &,&{{ -5}}~) \end{array} \\\\\\ % slope = m slope = {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-5-(-1)}{5-(-5)}\implies \cfrac{-5+1}{5+5}\implies \cfrac{-4}{10} \\\\\\ -\cfrac{2}{5}$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=-\cfrac{2}{5}[x-(-5)] \\\\\\ y+1=-\cfrac{2}{5}(x+5)\implies y+1=-\cfrac{2}{5}x-\cfrac{2}{\underline{5}}\cdot \underline{5}\implies y+1=-\cfrac{2}{5}x-2 \\\\\\ y+1-1=-\cfrac{2}{5}x-2-1\implies y=-\cfrac{2}{5}x-3$