If two lines have slopes m₁ = −4/3 and m₂ = −4/3 but different y-intercepts, what is the graphical conclusion?
Answer and explanation
Correct answer: No solution
The governing graphical criterion is the relationship between slopes and intercepts. Two distinct nonvertical lines with equal slopes have the same direction and therefore are parallel. Because their y-intercepts are different, they are not the same line; distinct parallel lines never meet at any point. Hence the pair has no solution, so option B is correct. A unique solution would require the lines to intersect, which normally occurs when their slopes differ. Infinitely many solutions would occur only if both equations represented the very same line, requiring matching intercepts as well. Perpendicular lines have slopes whose product is −1, but here the product is (−4/3)(−4/3) = 16/9, not −1.
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What is the correct answer to this question?
No solution
Why is this the correct answer?
The governing graphical criterion is the relationship between slopes and intercepts. Two distinct nonvertical lines with equal slopes have the same direction and therefore are parallel. Because their y-intercepts are different, they are not the same line; distinct parallel lines never meet at any point. Hence the pair has no solution, so option B is correct. A unique solution would require the lines to intersect, which normally occurs when their slopes differ. Infinitely many solutions would occur only if both equations represented the very same line, requiring matching intercepts as well. Perpendicular lines have slopes whose product is −1, but here the product is (−4/3)(−4/3) = 16/9, not −1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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