Question

Draw the graph of a line 2x + 3y = 6. From the graph, find the slope and y-intercept of the line.

Answer 1

2x + 3y = 6
3y = 6 - 2x

y = `(6)/(3) - (2)/(3)x`

∴ y = `2 - (2)/(3)x`

When x = 3, y = `2 - (2)/(3)(3)` = 0

When x = -3, y = `2 - (2)/(3)(-3)` = 4

When x = 0, y = `2 - (2)/(3)(0)` = 2

x	3	-3	0
y	0	4	2

Plotting the points (3, 0), (-3, 4) and (0, 2), we get line segment as shown in the figure.
∴ The y-intercept is 2.
Slope 

= `"Change in y"/"Change in x"`

= `(2 - 0)/(0 - 3)`

= `(2)/(-3)`

∴ Slope

= `(-2)/(3)`.