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 = (y_(2) - y_(1))/(x_(2) - x_(1)) = (11 - 1)/(5 - (-5)) = (10)/(5 + 5) = (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 = (y_(2) - y_(1))/(x_(2) - x_(1)) = (20 - (-1))/(-3 - 4) = (20 + 1)/(-7) = (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.