Find the slope of the line passing through the following pairs of points :

(i) (-2, -3) and (1, 2)

(ii) (-4, 0) and origin

(iii) (a, -b) and (b, -a)

(i) (-2, -3) and (1, 2)

By formula,

Slope (m) = $\dfrac{y$2 - y1}{x2 - x1}

Substituting values we get,

$m = \dfrac{2 - (-3)}{1 - (-2)} \\[1em] = \dfrac{2 + 3}{1 + 2} \\[1em] = \dfrac{5}{3}.$

Hence, slope = $\dfrac{5}{3}$.

(ii) (-4, 0) and origin

By formula,

Slope (m) = $\dfrac{y$2 - y1}{x2 - x1}

Substituting values we get,

$m = \dfrac{0 - 0}{0 - (-4)} \\[1em] = \dfrac{0}{0 + 4} \\[1em] = \dfrac{0}{4} = 0.$

Hence, slope = 0.

(iii) (a, -b) and (b, -a)

By formula,

Slope (m) = $\dfrac{y$2 - y1}{x2 - x1}

Substituting values we get,

$m = \dfrac{-a - (-b)}{b - a} \\[1em] = \dfrac{-a + b}{b - a} \\[1em] = \dfrac{b - a}{b - a} = 1.$

Hence, slope = 1.