Plot the points A(1, 1), B(4, 7) and C(4, 10) on a graph paper. Connect A and B, and also A and C.

Which segment appears to have steeper slope, AB or AC?

Justify your conclusion by calculating the slopes of AB and AC.

From graph,

AC appears to be steeper.

$\text{Slope of AB } = \dfrac{7 - 1}{4 - 1} \\[1em] = \dfrac{6}{3} = 2. \\[1em] \text{Slope of AC } = \dfrac{10 - 1}{4 - 1} \\[1em] = \dfrac{9}{3} = 3.$

Since, AC has greater slope.

Hence, proved AC has steeper slope.