Find the equation of the line with x-intercept 5 and a point on it (-3, 2).

When x-intercept = 5; corresponding point on the x-axis = (5, 0).

Slope of the line through (5, 0) and (-3, 2) = $\dfrac{2 - 0}{-3 - 5} = \dfrac{2}{-8} = -\dfrac{1}{4}$.

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = $-\dfrac{1}{4}(x - 5)$

⇒ 4y = -1(x - 5)

⇒ 4y = -x + 5

⇒ x + 4y = 5.

Hence, equation of line is x + 4y = 5.