For each equation, given below, find the slope and the y-intercept :

(i) 3x + 2y + 4 = 0

(ii) x - 3y - 8 = 0

(iii) x + y + 4 = 0

(iv) x = 3y + 2

(v) y = 5 - 4x

(vi) 2y + 5 = 0

(i) 3x + 2y + 4 = 0

⇒ 2y = - 3x - 4

⇒ y = $\dfrac{- 3x - 4}{2}$

⇒ y = $\dfrac{- 3x}{2} - \dfrac{4}{2}$

⇒ y = $\dfrac{- 3}{2} \text{ x } -2$

∴ Slope = coefficient of x = $\dfrac{-3}{2}$

And, y-intercept = constant term = -2

Hence, slope = $\dfrac{- 3}{2}$ and y-intercept = -2.

(ii) x - 3y - 8 = 0

⇒ 3y = x - 8

⇒ y = $\dfrac{x - 8}{3}$

⇒ y = $\dfrac{1}{3} \text{ x } - \dfrac{8}{3}$

∴ Slope = coefficient of x = $\dfrac{1}{3}$

And, y-intercept = constant term = $\dfrac{-8}{3}$

Hence, slope = $\dfrac{1}{3}$ and y-intercept = $\dfrac{-8}{3}$.

(iii) x + y + 4 = 0

⇒ y = -x - 4

∴ Slope = coefficient of x = -1

And, y-intercept = constant term = -4

Hence, slope = -1 and y-intercept = -4.

(iv) x = 3y + 2

⇒ 3y = x - 2

⇒ y = $\dfrac{x - 2}{3}$

⇒ y = $\dfrac{1}{3} \text{ x } - \dfrac{2}{3}$

∴ Slope = coefficient of x = $\dfrac{1}{3}$

And, y-intercept = constant term = $\dfrac{-2}{3}$

Hence, slope = $\dfrac{1}{3}$ and y-intercept = $\dfrac{-2}{3}$.

(v) y = 5 - 4x

⇒ y = -4x + 5

∴ Slope = coefficient of x = -4

And, y-intercept = constant term = 5

Hence, slope = -4 and y-intercept = 5.

(vi) 2y + 5 = 0

⇒ 2y = -5

⇒ y = $\dfrac{-5}{2}$

⇒ y = 0 + $\dfrac{-5}{2}$

∴ Slope = coefficient of x = 0

And, y-intercept = constant term = $\dfrac{-5}{2}$

Hence, slope = 0 and y-intercept = $\dfrac{-5}{2}$.