The slope of a line passing through (-1, 0) is 1.

Assertion (A): Its x-intercept and y-intercept are equal.

Reason (R): It makes an isosceles triangle with the coordinate axes.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

By point-slope form,

⇒ y - y₁ = m(x - x₁)

Equation of line passing through (-1, 0) and slope = 1 is :

⇒ y - 0 = 1[x - (-1)]

⇒ y = x + 1

⇒ x - y + 1 = 0

In order to find x-intercept, substitute y = 0 in the equation of line :

⇒ x - 0 + 1 = 0

⇒ x = -1

In order to find y-intercept, substitute x = 0 in the equation of line :

⇒ 0 - y + 1 = 0

⇒ y = 1

Thus, x-intercept and y-intercept are not equal.

So, assertion (A) is false.

The triangle are formed with the axes has vertices : (0, 0), (-1, 0) and (0, 1).

By distance formula,

Distance between two points = $\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}

$\text{Distance between (0, 0) and (-1, 0)} = \sqrt{(-1 - 0)^2 + (0 - 0)^2}\\[1em] = \sqrt{(-1)^2}\\[1em] = \sqrt{1}\\[1em] = 1 \\[1em] \text{Distance between (0, 0) and (0, 1)} = \sqrt{(0 - 0)^2 + (0 - 1)^2}\\[1em] = \sqrt{(-1)^2}\\[1em] = \sqrt{1}\\[1em] = 1$

Since,two sides are equal in length. Therefore, it is an isosceles triangle.

So, reason (R) is true.

Thus, Assertion (A) is false, Reason (R) is true.

Hence, option 2 is the correct option.