Question

Line A passes through the points (-5, 1) and (5, 11).

Line B passes through the points (4, -1) and (-3, 20).

Find the point where line A intersects line B.

A. X = 29/4, y =5/4


B. X = 5/4, y = 29/4


C. X = -5, y = -3


D. X = 1, = -3

Answer 1

Line A:$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{11 - 1}{5 - (-5)} = \frac{10}{5 + 5} = \frac{10}{10} = 1$
y - y₁ = m(x - x₁)
 y - 1 = 1(x - (-5))
 y - 1 = 1(x + 5)
 y - 1 = 1(x) + 1(5)
 y - 1 = x + 5
   + 1       + 1
       y = x + 6

Line B:$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{20 - (-1)}{-3 - 4} = \frac{20 + 1}{-7} = \frac{21}{-7} = -3$
   y - y₁ = m(x - x₁)
y - (-1) = -3(x - 4)
   y + 1 = -3(x) + 3(4)
   y + 1 = -3x + 12
       - 1          -    1
         y = -3x + 11

y = x + 6
y = -3x + 11

     x + 6 = -3x + 11
+ 3x        + 3x
   4x + 6 = 11
         - 6   - 6
         4x = 5
          4     4
           x = 1¹/₄
           y = x + 6
           y = 1¹/₄ + 6
           y = 7¹/₄
     (x, y) = (1¹/₄, 7¹/₄)

The answer is B.