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.
