If two lines have slopes m1 = 5/2 and m2 = 5/2 but different y-intercepts, what is the graphical conclusion?
Answer and explanation
Correct answer: No solution
The governing concept is the relationship between slopes and the number of intersections. Two non-identical lines with equal slopes have the same direction and therefore are parallel. Since the y-intercepts are different, the lines are not the same line; they are distinct parallel lines. Distinct parallel lines never meet, so their pair of equations has no common ordered pair and hence no solution. Therefore option B is correct. A unique solution would require different slopes so that the lines intersect once. Infinitely many solutions would occur only when both the slope and the intercept were equal, producing coincident lines. Perpendicular lines would require the product of their slopes to be −1, which is not true here.
Frequently asked questions
What is the correct answer to this question?
No solution
Why is this the correct answer?
The governing concept is the relationship between slopes and the number of intersections. Two non-identical lines with equal slopes have the same direction and therefore are parallel. Since the y-intercepts are different, the lines are not the same line; they are distinct parallel lines. Distinct parallel lines never meet, so their pair of equations has no common ordered pair and hence no solution. Therefore option B is correct. A unique solution would require different slopes so that the lines intersect once. Infinitely many solutions would occur only when both the slope and the intercept were equal, producing coincident lines. Perpendicular lines would require the product of their slopes to be −1, which is not true 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: Graphical method of finding solutions..
