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

(i) x + 3y + 5 = 0

(ii) 3x - y - 8 = 0

(iii) 5x = 4y + 7

(iv) x = 5y - 4

(v) y = 7x - 2

(vi) 3y = 7

(vii) 4y + 9 = 0

(i) x + 3y + 5 = 0

⇒ 3y = -x - 5

⇒ y = -$\dfrac{1}{3}x - \dfrac{5}{3}$

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

And, y-intercept = constant term = $\dfrac{-5}{3}$

Hence, the slope = $\dfrac{-1}{3}$ and y-intercept = $\dfrac{-5}{3}$.

(ii) 3x - y - 8 = 0

⇒ y = 3x - 8

∴ Slope = coefficient of x = 3

And, y-intercept = constant term = -8

Hence, the slope = 3 and y-intercept = -8.

(iii) 5x = 4y + 7

⇒ 4y = 5x - 7

⇒ y = $\dfrac{5}{4}$ x - $\dfrac{7}{4}$

∴ Slope = coefficient of x = $\dfrac{5}{4}$

And, y-intercept = constant term = $\dfrac{-7}{4}$

Hence, the slope = $\dfrac{5}{4}$ and y-intercept = $\dfrac{-7}{4}$.

(iv) x = 5y - 4

⇒ 5y = x + 4

⇒ y = $\dfrac{1}{5}$ x + $\dfrac{4}{5}$

∴ Slope = coefficient of x = $\dfrac{1}{5}$

And, y-intercept = constant term = $\dfrac{4}{5}$

Hence, the slope = $\dfrac{1}{5}$ and y-intercept = $\dfrac{4}{5}$.

(v) y = 7x - 2

∴ Slope = coefficient of x = 7

And, y-intercept = constant term = -2

Hence, the slope = 7 and y-intercept = -2.

(vi) 3y = 7

⇒ 3y = 0 $\times$ x + 7

⇒ y = 0 $\times$ x + $\dfrac{7}{3}$

∴ Slope = coefficient of x = 0

And, y-intercept = constant term = $\dfrac{7}{3}$

Hence, the slope = 0 and y-intercept = $\dfrac{7}{3}$.

(vii) 4y + 9 = 0

⇒ 4y = 0 $\times$ x - 9

⇒ y = 0 $\times$ x - $\dfrac{9}{4}$

∴ Slope = coefficient of x = 0

And, y-intercept = constant term = $\dfrac{-9}{4}$

Hence, the slope = 0 and y-intercept = $\dfrac{-9}{4}$.