Draw the graphs of the following linear equation.

2x + 3y = 6

Also find slope and y-intercept of this line.

Given,

⇒ 2x + 3y = 6

⇒ 3y = 6 - 2x

⇒ y = $\dfrac{6}{3} - \dfrac{2x}{3}$

⇒ y = $-\dfrac{2x}{3} + 2$ ………..(1)

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

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

x = 6, y = $2 - \dfrac{2 \times 6}{3} = 2 - \dfrac{12}{3}$ = 2 - 4 = -2.

Steps of construction :

1. Plot the points (0, 2), (3, 0) and (6, -2) on graph.

2. Join the points.

Comparing equation (1) with y = mx + c, we get :

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

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