Question

A line passes through the point (-4,-1) and has a slope of -3/2 . Write an equation in slope-intercept form for this line.

Answer 1

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{2} \\\\\\ \begin{array}ll \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{(-4)}) \implies y +1= -\cfrac{3}{2} (x +4) \\\\\\ y+1=-\cfrac{3}{2}x-6\implies {\Large \begin{array}{llll} y=-\cfrac{3}{2}x-7 \end{array}}`