If two lines have the same slope and the same intercept then what kind of lines will they be?
Answer and explanation
Correct answer: Coincident
A line written as y=mx+c is determined by its slope m and y-intercept c. If two lines have the same value of m and the same value of c, their equations are identical: y=m₁x+c₁ and y=m₁x+c₁. Therefore they are not two separate parallel lines; they lie exactly on top of each other and are called coincident lines. Every point on this common line satisfies both equations, so the corresponding pair has infinitely many solutions and is consistent and dependent. Distinct parallel lines have the same slope but different intercepts. Intersecting lines have different slopes, and perpendicular lines have slopes whose product is -1 when defined. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
Coincident
Why is this the correct answer?
A line written as y=mx+c is determined by its slope m and y-intercept c. If two lines have the same value of m and the same value of c, their equations are identical: y=m₁x+c₁ and y=m₁x+c₁. Therefore they are not two separate parallel lines; they lie exactly on top of each other and are called coincident lines. Every point on this common line satisfies both equations, so the corresponding pair has infinitely many solutions and is consistent and dependent. Distinct parallel lines have the same slope but different intercepts. Intersecting lines have different slopes, and perpendicular lines have slopes whose product is -1 when defined. Hence option C is correct.
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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