If two lines have the same slope and the same intercept, what kind of lines are they?
Answer and explanation
Correct answer: Coincident lines
A line can be written in slope-intercept form as
m y=mx+c
m, where
m m
m is the slope and
m c
m is the intercept on the y-axis. The slope determines the direction of the line, while the intercept determines its position. If two lines have equal slopes but different intercepts, they are distinct parallel lines. If both slope and intercept are equal, their equations describe the very same set of points, so the lines coincide.
Here both lines have the same value of
m m
m and the same value of
m c
m. Consequently, every point satisfying the first line also satisfies the second, and no separate intersection point can be identified. The lines are therefore coincident and the pair has infinitely many common solutions. Thus option B is correct. Distinct parallel lines would require equal slopes but unequal intercepts.
Frequently asked questions
What is the correct answer to this question?
Coincident lines
Why is this the correct answer?
A line can be written in slope-intercept form as
m y=mx+c
m, where
m m
m is the slope and
m c
m is the intercept on the y-axis. The slope determines the direction of the line, while the intercept determines its position. If two lines have equal slopes but different intercepts, they are distinct parallel lines. If both slope and intercept are equal, their equations describe the very same set of points, so the lines coincide.
Here both lines have the same value of
m m
m and the same value of
m c
m. Consequently, every point satisfying the first line also satisfies the second, and no separate intersection point can be identified. The lines are therefore coincident and the pair has infinitely many common solutions. Thus option B is correct. Distinct parallel lines would require equal slopes but unequal intercepts.
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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