9. Find the point of intersection of the lines: y = 4x + 1 and y = - 2x + 4 A. (2,9) B.(1/2,3) C. (1,2) D. (1/4,2)
2 answers:
Step-by-step explanation:
y = 4x + 1 and y = -2x + 4
4x + 1 = -2x + 4, 6x = 3, x = 0.5
When x = 0.5, y = 4(0.5) + 1 = 3.
The point of intersection is (0.5, 3). (B)
Step-by-step explanation:
y = 4x + 1
A.(2,9)
y = 4(2) + 1 = 9
y = 9.
y = 4x + 1
9 = 4x + 1
9 - 1 = 4x
8 = 4x => x = 8÷4 = 2
x = 2.
y = -2x + 4.
A.(2,9)
y = -2(2) + 4 = 0
y = 0.
y = - 2x + 4
0 = -2x + 4
0 - 4 = 2x
0 = 2x => x = 0 ÷ 2 = 0
x = 0.
y = 4x + 1
B.(1/2, 3)
y = 4(1/2) + 1
y = 4 ÷ 2 + 1 = 3
y = 3.
y = 4x + 1
3 = 4x + 1
3 - 1 = 4x
2 = 4x => x = 2 ÷ 4 = 1/2
x = 1/2.
y = - 2x + 4
B.(1/2, 3)
3 = - 2x + 4
3 - 4 = - 2x
- 1 = - 2x => x = 1/2
x = 1/2.
y = - 2x + 4
y = - 2(1/2) + 4
y = -2(0.5)+ 4
y = -1 + 4 = 3
y = 4x + 1
C.(1,2)
y = 4(1) + 1 = 5
y = 5.
y = 4x + 1
5 = 4x + 1
5 - 1 = 4x
4 = 4x => x = 4÷4 =1
x = 1.
y = -2x + 4
C.(1, 2)
y = - 2(1) + 4
y = - 2 + 4 = 2
y = 2.
2 = -2x + 4
2 - 4 = - 2x
- 2 = - 2x => x = 2÷2 = 1
x = 1.
y = 4x + 1
D.(1/4, 2)
y = 4(1/4) + 1
y = 4(0.25) + 1
y = 1 + 1 = 2
y = 2.
y = 4x + 1
2 = 4x + 1
2 - 1 = 4x
1 = 4x => x = 1/4
Point A is the point of intersection of the lines.
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