If two lines have slopes m₁ = −7/4 and m₂ = −7/4, but different y-intercepts, what is the graphical conclusion?
Answer and explanation
Correct answer: No solution
The governing concept is the graphical condition for a pair of linear equations. Two non-identical straight lines having equal slopes are parallel. Here m₁ = m₂ = −7/4, while the y-intercepts are different, so the lines cannot be the same line; they remain distinct parallel lines. Distinct parallel lines never meet at any point in the Cartesian plane. Since a common solution would be represented by an intersection point, the pair has no common solution. Option B is therefore correct. Option A would describe lines with unequal slopes that intersect once, option C would describe coincident lines with the same slope and the same intercept, and option D is incorrect because perpendicular lines have slopes whose product is −1, not equal slopes.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
The governing concept is the graphical condition for a pair of linear equations. Two non-identical straight lines having equal slopes are parallel. Here m₁ = m₂ = −7/4, while the y-intercepts are different, so the lines cannot be the same line; they remain distinct parallel lines. Distinct parallel lines never meet at any point in the Cartesian plane. Since a common solution would be represented by an intersection point, the pair has no common solution. Option B is therefore correct. Option A would describe lines with unequal slopes that intersect once, option C would describe coincident lines with the same slope and the same intercept, and option D is incorrect because perpendicular lines have slopes whose product is −1, not equal slopes.
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..
