Question

What is the equation of the line that passes through the point left bracket, 6, comma, minus, 1, right bracket(6,−1) and has a slope of minus, start fraction, 3, divided by, 2, end fraction−

2
3
​
?

Answer 1

`(\stackrel{x_1}{6}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{3}{2} \\\\\\ \begin{array}c \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}{6}) \implies y +1 = -\cfrac{3}{2} ( x -6) \\\\\\ y+1=-\cfrac{3}{2}x+9\implies {\Large \begin{array}{llll} y=-\cfrac{3}{2}x+8 \end{array}}`