What is the condition for two lines ax + by + c1 = 0 and ax + by + c2 = 0 to be

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Question: What is the condition for two lines ax + by + c1 = 0 and ax + by + c2 = 0 to be parallel?

Options:

Correct Answer: c1 = c2

Solution:

Two lines are parallel if their coefficients of x and y are proportional, which means c1 must equal c2.

What is the condition for two lines ax + by + c1 = 0 and ax + by + c2 = 0 to be parallel?

What is the condition for two lines ax + by + c1 = 0 and ax + by + c2 = 0 to be parallel?

Step 1: Identify the equations of the two lines. They are ax + by + c1 = 0 and ax + by + c2 = 0.
Step 2: Look at the coefficients of x and y in both equations. They are 'a' for x and 'b' for y.
Step 3: For two lines to be parallel, their slopes must be the same. The slope of a line in the form ax + by + c = 0 is -a/b.
Step 4: Since both lines have the same coefficients 'a' and 'b', their slopes are the same.
Step 5: The only difference between the two lines is the constant terms c1 and c2.
Step 6: For the lines to be parallel, c1 must not equal c2. If c1 equals c2, the lines are the same line, not just parallel.

Parallel Lines – Two lines are parallel if they have the same slope, which occurs when their coefficients of x and y are proportional.
Line Equation – The general form of a line equation is ax + by + c = 0, where a and b are the coefficients that determine the slope.