If two lines have different slopes, how many intersection points do they have?

If two lines have different slopes, how many intersection points do they have?

• A. The lines are parallel
• B. The lines have one intersecting point
• C. The lines are the same line
• D. No solution

Answer: (B)

When two lines have different slopes, they meet at exactly one point. This is because different slopes mean the lines aren’t parallel, so they must cross once as they extend across the plane. You can see this by solving their equations at the crossing: for example, if one line is y = 2x + 1 and the other is y = -x + 4, setting them equal gives 2x + 1 = -x + 4, which leads to x = 1 and y = 3. That shows there’s a single intersection point. If the slopes were the same, the lines would be parallel and either never meet or, if intercepts match, be the same line with infinitely many intersections. But with different slopes, the intersection count is exactly one.

When two lines have different slopes, they meet at exactly one point. This is because different slopes mean the lines aren’t parallel, so they must cross once as they extend across the plane. You can see this by solving their equations at the crossing: for example, if one line is y = 2x + 1 and the other is y = -x + 4, setting them equal gives 2x + 1 = -x + 4, which leads to x = 1 and y = 3. That shows there’s a single intersection point. If the slopes were the same, the lines would be parallel and either never meet or, if intercepts match, be the same line with infinitely many intersections. But with different slopes, the intersection count is exactly one.