Solution:

Given, x-intercept of a line is 6

So,

The line will pass through the point (6, 0)

Also given, the y -intercept of the line is -4 ⇒ c = -4

So, the line will pass through the point (0, -4)

Now,

Slope, m = m = y₂ – y₁/ x₂ – x₁

m = (-4 – 0)/(0 – 6) = -4/-6 = 2/3

Thus, the equation of the line is given by

y = mx + c

y = (2/3)x + (-4)

3y = 2x – 12

⇒ 2x – 3y – 12 = 0