Question

Which is an equation in point-slope form of the line that passes through the points

(4, 5) and (−3, −1) ?
A) y+3=7/6(x+1)
B) y+1=6/5(x+3)
C) y+1=6/7(x+3)
D) y−1=6/7(x−3)

Answer 1

the slope (m) is (5 - -1) / 4 --3 = 6/7

y - y1 = (6/7)(x - x1)

y - -1 = (6/7)( x - -3)

y + 1 = 6/7(x + 3)

Answer 2

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{-1}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ -7 } \implies \cfrac{6}{7}`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_2}{(-1)}=\stackrel{m}{\cfrac{6}{7}}(x-\stackrel{x_2}{(-3)})\implies \boxed{y+1=\cfrac{6}{7}(x+3)}`