Question

A line passes through (-7,-5) and (-5,4). Write an equation for the line in point-slope form. Rewrite the equation in standard form using integers

Answer 1

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -7 &,& -5~) % (c,d) &&(~ -5 &,& 4~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-(-5)}{-5-(-7)}\implies \cfrac{4+5}{-5+7}\implies \cfrac{9}{2}$

$\bf \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{9}{2}[x-(-7)] \\\\\\ y+5=\cfrac{9}{2}(x+7)\impliedby \textit{now let's multiply both sides by }\stackrel{LCD}{2} \\\\\\ 2(y+5)=2\left[ \cfrac{9}{2}(x+7)\right]\implies 2y+10=9(x+7) \\\\\\ 2y+10=9x+63\implies \stackrel{standard~form}{-9x+2y=53}$