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Line l₁ passes through (-1,1) and (6,15). Another line l₂ passes through (0,-12) and (3,3). Determine the coordinate of the point at which they intersect.

User Christos
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Final answer:

The intersection of lines l₁ and l₂ is found by determining the equations from the given points and solving the system. The intersection point is (5, 13).

Step-by-step explanation:

To find the intersection of the lines l₁ and l₂, we need to determine the equations of these lines using the points given and then solve the system of equations. For line l₁ which passes through (-1,1) and (6,15), we find the slope m as Δy/Δx = (15-1)/(6+1) = 14/7 = 2. The equation of the line in slope-intercept form is y = mx + b. Substituting one of the points and the slope into this equation gives us 1 = 2(-1) + b, resulting in b = 3. Thus, the equation for line l₁ is y = 2x + 3.

For line l₂, which passes through (0,-12) and (3,3), its slope is Δy/Δx = (3+12)/(3-0) = 15/3 = 5. Using the y-intercept already given by the point (0,-12), the equation for line l₂ is y = 5x - 12.

Now we solve the system:

  • y = 2x + 3
  • y = 5x - 12

By setting the equations equal to each other, we have 2x + 3 = 5x - 12. Solving for x gives x = 5. Substituting x = 5 into either of the original equations gives us y = 2(5) + 3 = 13. Therefore, the intersection point is (5, 13).

User Indrani
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7.8k points
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