Find the equation of a line:

(i) Whose slope is 4 and which passes through the point (3, 7)

(ii) Whose slope is –3 and which passes through the point (–2, 3)

(i) By point-slope form,

Equation of line : y - y₁ = m(x - x₁)

Substituting values we get,

⇒ y - 7 = 4(x - 3)

⇒ y - 7 = 4x - 12

⇒ y = 4x - 12 + 7

⇒ y = 4x - 5

⇒ 4x - y = 5.

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

(ii) By point-slope form,

Equation of line : y - y₁ = m(x - x₁)

Substituting values we get,

⇒ y - 3 = -3(x - (-2))

⇒ y - 3 = -3(x + 2)

⇒ y - 3 = -3x - 6

⇒ y = -3x - 6 + 3

⇒ y = -3x - 3

⇒ 3x + y + 3 = 0

Hence, equation of the line is 3x + y + 3 = 0.