Question

1. The equation of a line with x-intercept 3 and y-intercept 2 is 2x + 3y = 12.
2. Two lines with slopes m₁ and m₂ are parallel if m₁ m₂ = −1.

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Neither (i) nor (ii)

Explanation:

⇒ Going through (i) statement,

To find the equation with intercepts x = 3 and y = 2, we use the formula `x/a + y/b = 1`:

`x/3 + y/2 = 1`

Multiply the whole equation by 6 because of the common LCM to clear fractions:

`6(x/3) + 6(y/2) = 1(6)`

2x + 3y = 6

The statement says 2x + 3y = 12, so it is incorrect.

⇒ Going through (ii) statement,

Two lines are parallel if their slopes are equal (m₁ = m₂).

The condition given (m₁ m₂ = −1) is actually the rule for perpendicular lines.

So, this statement is also invalid.