Intersection of Two Lines
This calculator helps you find the point where two lines meet. Just enter the slope and y-intercept for each line, and we'll show you the (x, y) coordinates of their intersection.
Enter the slope for the first line (e.g., 2)
Enter the y-intercept for the first line (e.g., 3)
Enter the slope for the second line (e.g., -1)
Enter the y-intercept for the second line (e.g., 6)
This calculator helps you find the point where two lines meet. Just enter the slope and y-intercept for each line, and we'll show you the (x, y) coordinates of their intersection.
For two lines in slope-intercept form: Line 1: y = m₁x + b₁ Line 2: y = m₂x + b₂ To find the intersection, set y₁ = y₂: m₁x + b₁ = m₂x + b₂ (m₁ - m₂)x = b₂ - b₁ x = (b₂ - b₁) / (m₁ - m₂) Then substitute x back into either equation to find y: y = m₁x + b₁
Let's say you have two lines: Line 1: y = 2x + 3 (m₁=2, b₁=3) Line 2: y = -1x + 6 (m₂=-1, b₂=6) Using the formula: x = (6 - 3) / (2 - (-1)) x = 3 / 3 x = 1 Now, find y using Line 1: y = 2(1) + 3 y = 5 The intersection point is (1, 5).
The intersection of two lines is the single point (x, y) where they cross each other on a coordinate plane. At this point, both lines share the same x and y values.
If your equations are in a different form (like Ax + By = C), you'll need to rearrange them into the slope-intercept form (y = mx + b) first. Isolate 'y' on one side of the equation to identify the slope (m) and y-intercept (b).
If two lines are parallel, they have the same slope (m) but different y-intercepts (b). They will never cross, so there is no intersection point. Our calculator will tell you if the lines are parallel.
If two lines have the same slope (m) AND the same y-intercept (b), they are identical. This means they are the exact same line, and they intersect at infinitely many points. The calculator will indicate this situation.
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