$\text{The slope of the line joining the points } (x_1,y_1) \text{ and } (x_2,y_2) \text{ is given by } m=\dfrac{y_2-y_1}{x_2-x_1}$.So, the slope of the line joining the points \(\left(4,-6\right)\) and \(\left(10,3\right)\) is \(\dfrac{\left(3\right)-\left(-6\right)}{\left(10\right)-\left(4\right)}\) = \(\dfrac{3+6}{10-4}\) = \(\dfrac{9}{6}\) = \(\dfrac{3}{2}\)The slope is positive, so the line is rising from left to right.