If two lines have the same slope and the same (y)-intercept, what will be the type of pair?
Answer and explanation
Correct answer: Consistent and dependent
The slope of a non-vertical line describes its steepness, and the y-intercept tells where it crosses the y-axis. If two lines have the same slope, they are parallel or identical. If their y-intercepts are also the same, they pass through the same point on the y-axis and have the same direction. Consequently, they are not merely parallel; they coincide completely.
Coincident lines have every point in common. Therefore the pair has infinitely many solutions and is called consistent and dependent. Option C is correct. An inconsistent pair has no common point, as with distinct parallel lines. A consistent independent pair has one common point, which does not apply here.
Frequently asked questions
What is the correct answer to this question?
Consistent and dependent
Why is this the correct answer?
The slope of a non-vertical line describes its steepness, and the y-intercept tells where it crosses the y-axis. If two lines have the same slope, they are parallel or identical. If their y-intercepts are also the same, they pass through the same point on the y-axis and have the same direction. Consequently, they are not merely parallel; they coincide completely.
Coincident lines have every point in common. Therefore the pair has infinitely many solutions and is called consistent and dependent. Option C is correct. An inconsistent pair has no common point, as with distinct parallel lines. A consistent independent pair has one common point, which does not apply here.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
