Find the equation of a straight line passing th... - SS2 Mathematics Gradient of Lines Question

\[\frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\]

\[\frac{y - 3}{x - ( - 4)} = \frac{- 5 - 3}{2 - ( - 4)}\]

\[\frac{y - 3}{x + 4} = \frac{- 8}{2 + 4}\]

\[\frac{y - 3}{x + 4} = \frac{- 8}{6}\]

\[6(y - 3) = - 8(x + 4)\]

\[6y - 18 = - 8x - 32\]

\[6y = - 8x - 32 + 18\]

\[6y = - 8x - 14\]

\[y = \frac{- 8}{6}x - \frac{14}{6}\]

\(y = \frac{- 4}{3}x - \frac{7}{3}\) is the required equation