Find the intersection of the line through (0, 1) and (4.4, 2) and the line through (1.9, 3) and (5.3, 0). (Round your answers to the nearest tenth.)

Question

(x, y) =

Answer 1

(0 , 1) , (4.4 , 2).(1.9 , 3)(5.3 , 0).
m1 = (2 - 1) / (4.4 - 0)
= 1 / 4.4 = 0.227,
y = mx + b,
1 = 0.227*0 + b,
b = 1.
Eq1. y = 0.227x + 1.

(1.9 , 3) , (5.3 , 0),

m2 = (0 - 3) / (5,3 - 1.9),
= -3 / 3.4 = -0.88,
y = mx + b,
3 = -0.88*1.9 + b,
3 = -1.68 + b,
3 + 1.68 = b,
b = 4.68.
Eq2. y = -0.88x + 4.68.

Substitute Eq1 for y in Eq2:
0.227x + 1 = -0.88x + 4.68,
0.227x + 0.88x = 4.68 - 1,
1.107x = 3.68,
x = 3.68 /1.107 = 3.32.

Substitute 3.32 for x in Eq1:
y = 0.227*3.32 + 1,
= 0.755 + 1,
= 1.76.

Solution set: (x , y) = (3.3 , 1.8) =
Point where the 2 lines intersect.