A line passes through the point (5, 7) and has gradient $\frac{2}{3}$. Find the x-coordinate of a point on the line when y = 13.

Let the x coordinate of the be 'x', when y = 13             

Thus,

The gradient of the line $=\frac{(y_2-y_1)}{(x_2-x_1)}$    

From the figure,

The gradient of the line $=\frac{6}{\mathrm{x}-5}$    

 $\begin{array}{c}\Rightarrow \frac{2}{3} = \frac{6}{\mathrm{x} - 5}\end{array}$

$\begin{array}{c}\Rightarrow 2\mathrm{x} - 10 = 18\end{array}$

$\begin{array}{cc}\Rightarrow 2\mathrm{x} = 28& \end{array}$

$\Rightarrow \mathrm{x} = 14$

Thus, the coordinate of the x-axis is 14.