Find the slope and y-intercept of the following lines :

(i) x - 2y - 1 = 0

(ii) 4x - 5y - 9 = 0

(iii) 3x + 5y + 7 = 0

(iv) $\dfrac{x}{3} + \dfrac{y}{4} = 1$

(v) y - 3 = 0

(vi) x - 3 = 0

(i) The equation of line is

⇒ x - 2y - 1 = 0
⇒ 2y = x - 1
⇒ y = $\dfrac{x}{2} - \dfrac{1}{2}.$

Comparing the above equation with y = mx + c, we get,

m = $\dfrac{1}{2}$ and c = $-\dfrac{1}{2}$.

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

(ii) The equation of line is

⇒ 4x - 5y - 9 = 0
⇒ 5y = 4x - 9
⇒ y = $\dfrac{4x}{5} - \dfrac{9}{5}.$

Comparing the above equation with y = mx + c, we get,

m = $\dfrac{4}{5}$ and c = $-\dfrac{9}{5}$.

Hence, the slope of the line = $\dfrac{4}{5}$ and y-intercept = $-\dfrac{9}{5}$.

(iii) The equation of line is

⇒ 3x + 5y + 7 = 0
⇒ 5y = -3x - 7
⇒ y = $-\dfrac{3x}{5} - \dfrac{7}{5}.$

Comparing the above equation with y = mx + c, we get,

m = $-\dfrac{3}{5}$ and c = $-\dfrac{7}{5}$.

Hence, the slope of the line = $-\dfrac{3}{5}$ and y-intercept = $-\dfrac{7}{5}$.

(iv) The equation of line is

$\Rightarrow \dfrac{x}{3} + \dfrac{y}{4} = 1 \\[1em] \Rightarrow \dfrac{4x + 3y}{12} = 1 \\[1em] \Rightarrow 4x + 3y = 12 \\[1em] \Rightarrow 3y = -4x + 12 \\[1em] \Rightarrow y = -\dfrac{4}{3}x + \dfrac{12}{3} \\[1em] \Rightarrow y = -\dfrac{4}{3}x + 4.$

Comparing the above equation with y = mx + c, we get,

m = $-\dfrac{4}{3}$ and c = 4.

Hence, the slope of the line = $-\dfrac{4}{3}$ and y-intercept = 4.

(v) The equation of line is

⇒ y - 3 = 0
⇒ y = 3
⇒ y = 0.x + 3

Comparing the above equation with y = mx + c, we get,

m = 0 and c = 3.

Hence, the slope of the line = 0 and y-intercept = 3.

(vi) The equation of line is

⇒ x - 3 = 0
⇒ x = 3.

Here, the slope cannot be defined as the line does not meet y-axis.

Hence, the slope of the line is undefined and there is no y-intercept as line does not meet y-axis.