Find the equation of the line, whose :

(i) x-intercept = 5 and y-intercept = 3

(ii) x-intercept = -4 and y-intercept = 6

(iii) x-intercept = -8 and y-intercept = -4

(i) x-intercept = 5 and y-intercept = 3

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

When y-intercept = 3; corresponding point on the y-axis = (0, 3).

$\text{Slope }= \dfrac{3 - 0}{0 - 5} = -\dfrac{3}{5}.$

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = $-\dfrac{3}{5}$(x - 5)

⇒ 5y = -3(x - 5)

⇒ 5y = -3x + 15

⇒ 3x + 5y = 15.

Hence, equation of line is 3x + 5y = 15.

(ii) x-intercept = -4 and y-intercept = 6

When x-intercept = -4; corresponding point on the x-axis = (-4, 0)

When y-intercept = 6; corresponding point on the y-axis = (0, 6).

$\text{Slope }= \dfrac{6 - 0}{0 - (-4)} = \dfrac{6}{4}.$

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = $\dfrac{6}{4}$[x - (-4)]

⇒ y = $\dfrac{3}{2}$(x + 4)

⇒ 2y = 3x + 12

⇒ 2y - 3x = 12

⇒ 2y = 3x + 12

Hence, equation of line is 2y = 3x + 12.

(iii) x-intercept = -8 and y-intercept = -4

When x-intercept = -8; corresponding point on the x-axis = (-8, 0)

When y-intercept = -4; corresponding point on the y-axis = (0, -4).

$\text{Slope }= \dfrac{-4 - 0}{0 - (-8)} = \dfrac{-4}{8} = -\dfrac{1}{2}.$

By point-slope form,

⇒ y - y₁ = m(x - x₁)

⇒ y - 0 = $-\dfrac{1}{2}$[x - (-8)]

⇒ y = $-\dfrac{1}{2}$(x + 8)

⇒ 2y = -x - 8

⇒ 2y + x + 8 = 0.

Hence, equation of line is x + 2y + 8 = 0.