Find the equation of the line through the point (-1, 3) and parallel to the line joining the points (0, -2) and (4, 5).

The slope of the line passing through two points (x₁, y₁) and (x₂, y₂) is given by

Slope = $\dfrac{y$2 - y1}{x2 - x1}.

Slope of the line joining the points (0, -2) and (4, 5) is,

$= \dfrac{5 + 2}{4 - 0} \\[1em] = \dfrac{7}{4}.$

∴ Slope of line parallel to the line joining (0, -2) and (4, 5) = $\dfrac{7}{4}$

The equation of the line having slope $\dfrac{7}{4}$ and passing through (-1, 3) can be given by point-slope form i.e.,

$\Rightarrow y - y$1 = m(x - x1) \\[1em] \Rightarrow y - 3 = \dfrac{7}{4}(x - (-1)) \\[1em] \Rightarrow 4(y - 3) = 7(x + 1) \\[1em] \Rightarrow 4y - 12 = 7x + 7 \\[1em] \Rightarrow 7x - 4y + 19 = 0.

Hence, the equation of the line through the point (-1, 3) and parallel to the line joining the points (0, -2) and (4, 5) is 7x - 4y + 19 = 0.