Find the equation of a line passing through :

(i) (0, 1) and (1, 2)

(ii) (-1, -4) and (3, 0)

(i) (0, 1) and (1, 2)

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

Substituting values we get,

$m = \dfrac{2 - 1}{1 - 0} = \dfrac{1}{1} = 1. \\[1em] \text{Equation } : y - y$1= m(x - x1) \\[1em] \Rightarrow y - 1 = 1(x - 0) \\[1em] \Rightarrow y - 1 = x \\[1em] \Rightarrow y = x + 1.

Hence, equation of line is y = x + 1.

(ii) (-1, -4) and (3, 0)

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

Substituting values we get,

$m = \dfrac{0 - (-4)}{3 - (-1)} = \dfrac{0 + 4}{3 + 1} = \dfrac{4}{4} = 1. \\[1em] \text{Equation } : y - y$1= m(x - x1) \\[1em] \Rightarrow y - (-4) = 1(x - (-1)) \\[1em] \Rightarrow y + 4 = x + 1 \\[1em] \Rightarrow y = x + 1 - 4 \\[1em] \Rightarrow y = x - 3.

Hence, equation of line is y = x - 3.