Answer: Option A
To determine whether the given lines x + 2y - 9 = 0 and 3x + 6y + 8 = 0 are parallel or perpendicular, we need to compare their slopes. The slope of a line can be found using the formula:
slope = - coefficient of x / coefficient of y
Let's find the slope of the first line x + 2y - 9 = 0:
slope = - coefficient of x / coefficient of y= -1 / 2
Now let's find the slope of the second line 3x + 6y + 8 = 0:
slope = - coefficient of x / coefficient of y= -3 / 6= -1 / 2
Since both slopes are the same (-1/2), we can conclude that the given lines are parallel to each other. Therefore, the correct answer is option A.
Here are some key points to remember about parallel lines:

• Two lines are parallel if and only if they have the same slope.
• If two lines are parallel, they never intersect, no matter how far they are extended.
• The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
• If two lines are parallel, they have the same slope but different y-intercepts.
• To find the equation of a line given its slope and a point on the line, we can use the point-slope form of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.