You can find the value of k by using the slope formula, m = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex], where m is the slope and [tex] x_{1}[/tex], [tex] y_{1} [/tex], [tex] x_{2} [/tex], and [tex] y_{2} [/tex] are coordinate pairs on the line.
m = [tex] \frac{y_{2} - y_{1}}{x_{2} - x_{1}} [/tex] Plug in the values
-1 = [tex] \frac{3k - 4k}{k + 2 - k} [/tex] Subtract 3k and 4k
-1 = [tex] \frac{-k}{k + 2 - k} [/tex] Subtract k and k
-1 = [tex] \frac{-k}{2} [/tex] Multiply both sides by 2
-2 = -k Divide both sides by -1
2 = k
Now, replace two with k in the coordinates to figure out the actual numbers.
(k, 4k) and (k + 2, 3k) Plug in 2
(2, 4(2)) and (2 + 2, 3(2)) Simplify
(2, 8) and (4, 6)
Now, choose one of those coordinates and plug it into the point-slope equation ([tex]y - y_{1} = m (x - x_{1})[/tex]). I'll use (2, 8).
[tex]y - y_{1} = m (x - x_{1})[/tex] Plug in slope and the coordinate
y - 8 = -1 (x - 2)
