A straight line passes through the point of intersection of x + 2y + 2 = 0 and 2x - 3y - 3 = 0. It cuts equal intercepts in the fourth quadrant. What is the sum of the absolute values of the intercepts?

Concept:

1. A positive slope means y increases as x increases (visually, the line moves up as you go from left to right).
2. A negative slope means y decreases as x increases (visually, the line moves down as you go from left to right).

Calculation:

Given:

x + 2y + 2 = 0      ------(i)

2x - 3y - 3 = 0      ------(ii)

By solving (i) and (ii) we get the point of intersection of the lines.

So x = 0 and y = -1

The point of intersection is (0, -1)

Given that the line makes equal intercepts with axes. So slope (m) can be tan θ = 1

or -1 but it is in the fourth quadrant so, it is positive.

Then the equation of the line is y - y₁ = m(x - x₁)

⇒ y - (-1) = 1(x - 0)

⇒ y + 1 = x

⇒ x - y = 1

From this equation, the intercept on the x and y axes are 1 and -1 respectively.

∴ The sum of the absolute values of the intercepts = 2.