Three straight lines x + y – 3 = 0, x + y + 2 = 0 and 3x + 3y – 7 = 0 are:

Correct option is D

Given:

The equations of the three straight lines are:

x + y - 3 = 0

x + y + 2 = 0

3x + 3y - 7 = 0

Formula Used:
The general form of the equation of a straight line is:

Ax + By + C = 0

The slope of the line m is given by:

m $$= -\frac{A}{B}$$​

Solution:

For the first line x + y - 3 = 0: The equation can be rewritten as:

x + y = 3

So, the slope $$m_1$$​ is:

​$$m_1 = -\frac{1}{1} = -1$$​​

For the second line x + y + 2 = 0: The equation can be rewritten as:

x + y = -2

So, the slope $$m_2$$​ is:

​$$m_2 = -\frac{1}{1} = -1$$​​

For the third line 3x + 3y - 7 = 0: The equation can be rewritten as:

$$3x + 3y = 7 \quad \text{or} \quad x + y = \frac{7}{3}$$​

​$$m_3 = -\frac{1}{1} = -1$$​​

All three lines have the same slope ($$m_1 = m_2 = m_3 = -1$$​), which means they are parallel.