If two lines have the same slope but different (y)-intercepts, what will be the nature of the pair?
Answer and explanation
Correct answer: Inconsistent
The slope tells the direction of a line, while the y-intercept tells where it crosses the y-axis. Lines with the same slope move in the same direction. If their y-intercepts are different, they start at different heights and therefore cannot be the same line. They remain separate and parallel.
Because distinct parallel lines never meet, there is no ordered pair satisfying both linear equations. In the language of systems, the pair is inconsistent and has zero solutions. It is not dependent or infinitely solvable; those descriptions apply when both equations represent the same line. Therefore the correct choice is option B, inconsistent.
Frequently asked questions
What is the correct answer to this question?
Inconsistent
Why is this the correct answer?
The slope tells the direction of a line, while the y-intercept tells where it crosses the y-axis. Lines with the same slope move in the same direction. If their y-intercepts are different, they start at different heights and therefore cannot be the same line. They remain separate and parallel.
Because distinct parallel lines never meet, there is no ordered pair satisfying both linear equations. In the language of systems, the pair is inconsistent and has zero solutions. It is not dependent or infinitely solvable; those descriptions apply when both equations represent the same line. Therefore the correct choice is option B, inconsistent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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