Mathematics

Mathematics

Problem

Line 1 passes through (0,3)(0,3) and (6,0)(6,0). Line 2 passes through (0,1)(0,1) and (4,0)(4,0). Determine the coordinates of the point where the two lines meet.
Intuitive explanation

Both lines are defined by two points, so you can write their equations in slope-intercept or standard form. The key insight is that the intersection point must satisfy both equations simultaneously—it's the one (x,y)(x, y) pair that works for Line 1 and Line 2 at the same time. Find each line's equation, then solve the system to find where they cross.

Intuitive explanation

Both lines are defined by two points, so you can write their equations in slope-intercept or standard form. The key insight is that the intersection point must satisfy both equations simultaneously—it's the one (x,y)(x, y) pair that works for Line 1 and Line 2 at the same time. Find each line's equation, then solve the system to find where they cross.

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