Gradient of Lines - SS2 Mathematics Past Questions and Answers - page 1

\(\frac{\mathrm{\Delta}y}{\mathrm{\Delta}x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{3 - 3}{5 - 1} = \frac{0}{4} = 0\) 

\[y = mx + c\]

\[y = \frac{1}{2}x + 6\]

\(2y = x + 12\) is the required equation

\[y - y_{1} = m(x - x_{1})\]

\[y - 0 = - 1(x - 3)\]

\(y = - x + 3\) is the required equation

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

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

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

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

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

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

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

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

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

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

Comparing \(y = mx + c\) with \(y = 3x + 2\)

\(m = 3\), \(y\)-intercept \(= 2\)

\(x\)-intercept\(= \frac{- c}{m} = \ \frac{- 2}{3}\)