Draw the graphs of the following linear equation.

2x - 3y = 4

Also find slope and y-intercept of this line.

Given,

⇒ 2x - 3y = 4

⇒ 3y = 2x - 4

⇒ y = $\dfrac{2x - 4}{3}$

⇒ y = $\dfrac{2}{3}x - \dfrac{4}{3}$ ……..(1)

When x = -1, y = $\dfrac{2}{3} \times -1 - \dfrac{4}{3} = -\dfrac{2}{3} - \dfrac{4}{3} = -\dfrac{6}{3}$ = -2,

x = 2, y = $\dfrac{2}{3} \times 2 - \dfrac{4}{3} = \dfrac{4}{3} - \dfrac{4}{3}$ = 0,

x = 5, y = $\dfrac{2}{3} \times 5 - \dfrac{4}{3} = \dfrac{10}{3} - \dfrac{4}{3} = \dfrac{6}{3}$ = 2.

Steps of construction :

1. Plot the points (-1, -2), (2, 0) and (5, 2) on graph.

2. Join the points.

Comparing equation (1) with y = mx + c.

m = $\dfrac{2}{3}$ and c = $-\dfrac{4}{3}$.

Hence, the slope of line = $\dfrac{2}{3}$ and y intercept = $-\dfrac{4}{3}$.