+26387 Find v if the gradient between the points (5,2) and (11,v) is 3
\(\begin{array}{|rcl|} \hline P_1 = \binom{5}{2} \qquad x_1 = 5 \qquad y_1 = 2\\ P_2 = \binom{11}{v} \qquad x_2 = 11 \qquad y_2 = v\\ \hline \text{gradient} &=& 3 \\ \text{gradient} &=& \frac{\Delta y}{\Delta x} \\ 3 &=& \frac{y_2-y_1}{x_2-x_1} \\ 3 &=& \frac{v-2}{11-5} \\ 3 &=& \frac{v-2}{6} \\ 3\cdot 6 &=& v-2 \\ 18 &=& v-2 \\ 18+2 &=& v \\ 20 &=& v \\ \mathbf{v} &\mathbf{=}& \mathbf{20} \\ \hline \end{array} \)
