In which pair do both lines have equal slopes but different y-intercepts?
Answer and explanation
Correct answer: y = 2x + 5 and y = 2x − 3
The governing concept is the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. In option A, both equations have m = 2, so their slopes are equal, while their intercepts are c = 5 and c = −3, which are different. Therefore the lines never meet and are distinct parallel lines. Option B has opposite slopes, so it does not satisfy the condition. In option C the slopes are 1 and 2, so they are unequal and the lines intersect. Option D has equal slopes and equal intercepts, meaning it describes the same line rather than two distinct lines. Thus option A is the only correct choice.
Frequently asked questions
What is the correct answer to this question?
y = 2x + 5 and y = 2x − 3
Why is this the correct answer?
The governing concept is the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept. In option A, both equations have m = 2, so their slopes are equal, while their intercepts are c = 5 and c = −3, which are different. Therefore the lines never meet and are distinct parallel lines. Option B has opposite slopes, so it does not satisfy the condition. In option C the slopes are 1 and 2, so they are unequal and the lines intersect. Option D has equal slopes and equal intercepts, meaning it describes the same line rather than two distinct lines. Thus option A is the only correct choice.
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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