You can find the value of k by using the slope formula, m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\), where m is the slope and \(x_{1}\), \(y_{1}\), \(x_{2}\), and \(y_{2}\) are coordinate pairs on the line.
m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\) Plug in the values
-1 = \(\frac{3k - 4k}{k + 2 - k}\) Subtract 3k and 4k
-1 = \(\frac{-k}{k + 2 - k}\) Subtract k and k
-1 = \(\frac{-k}{2}\) 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 (\(y - y_{1} = m (x - x_{1})\)). I'll use (2, 8).
\(y - y_{1} = m (x - x_{1})\) Plug in slope and the coordinate
y - 8 = -1 (x - 2)
