Draw the graph of the equation 3x - 4y = 12. From the graph, find :

(i) the value of y when x = -4

(ii) the value of x when y = 3.

Given,

⇒ 3x - 4y = 12

⇒ 4y = 3x - 12

⇒ y = $\dfrac{3x - 12}{4}$

⇒ y = $\dfrac{3}{4}x - 3$.

When x = 0, y = $\dfrac{3}{4} \times 0 - 3$ = 0 - 3 = -3,

x = 4, y = $\dfrac{3}{4} \times 4 - 3$ = 3 - 3 = 0,

x = 8, y = $\dfrac{3}{4} \times 8 - 3 = \dfrac{24}{4} - 3$ = 6 - 3 = 3.

Steps of construction :

1. Plot the points (0, -3), (4, 0) and (8, 3) on graph.

2. Join the points.

(i) Steps of construction :

1. Take a point N (x = -4) and draw a line parallel to y-axis, touching the graph at point M.

2. From M draw a line parallel to x-axis touching y-axis at point O (y = -6).

Hence, when x = -4, the value of y is -6.

(ii) Steps of construction :

1. Take a point P (y = 3) and draw a line parallel to x-axis, touching the graph at point R.

2. From R draw a line parallel to y-axis touching x-axis at point Q (x = 8).

Hence, when y = 3, the value of x is 8.