Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Line A passes through points (-1, 5) and (3, -1). Line B passes through points (7, 2) and (6, -1). At what point does line A intersect line B?

Answer 1

Line A
slope = (-1 - 5)/(3+1) = -6/4 = -3/2
y = mx + b
5 = -3/2(-1) + b
b = 5 - 3/2
b = 7/2
equation of line A: y = -3/2x + 7/2

Line B
slope = (-1 - 2)/(6-7) = -3/-1 = 3
y = mx + b
2 = 3(7) + b
b = 2- 21
b = - 19
equation of line B: y = 3x -19

line A intersect line B when -3/2x + 7/2 = 3x -19
so
-3/2x + 7/2 = 3x -19
3x + 3/2x = 19 + 7/2
9/2x = 45/2
x = (45/2) * (2/9)
x = 5

y = 3x - 19 = 3(5) -19 = 15 -19 = -4

(5 , -4)

answer
line A intersect line B at (5, -4)