Answer :
To determine which point lies on the line described by the equation [tex]\( y + 3 = 2(x - 1) \)[/tex], we must check each point to see if it satisfies the equation. The points given are:
A. (2, 1)
B. (1, -4)
C. (0, 0)
D. (-1, -6)
E. (2, 9)
F. (1, -3)
We'll check each point one by one.
### Checking Point A: (2, 1)
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[ 1 + 3 = 2(2 - 1) \][/tex]
[tex]\[ 4 = 2 \times 1 \][/tex]
[tex]\[ 4 = 2 \][/tex]
This point does not lie on the line.
### Checking Point B: (1, -4)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -4 \)[/tex] into the equation:
[tex]\[ -4 + 3 = 2(1 - 1) \][/tex]
[tex]\[ -1 = 2 \times 0 \][/tex]
[tex]\[ -1 = 0 \][/tex]
This point does not lie on the line.
### Checking Point C: (0, 0)
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ 0 + 3 = 2(0 - 1) \][/tex]
[tex]\[ 3 = 2 \times -1 \][/tex]
[tex]\[ 3 = -2 \][/tex]
This point does not lie on the line.
### Checking Point D: (-1, -6)
Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -6 \)[/tex] into the equation:
[tex]\[ -6 + 3 = 2(-1 - 1) \][/tex]
[tex]\[ -3 = 2 \times -2 \][/tex]
[tex]\[ -3 = -4 \][/tex]
This point does not lie on the line.
### Checking Point E: (2, 9)
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 9 \)[/tex] into the equation:
[tex]\[ 9 + 3 = 2(2 - 1) \][/tex]
[tex]\[ 12 = 2 \times 1 \][/tex]
[tex]\[ 12 = 2 \][/tex]
This point does not lie on the line.
### Checking Point F: (1, -3)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -3 \)[/tex] into the equation:
[tex]\[ -3 + 3 = 2(1 - 1) \][/tex]
[tex]\[ 0 = 2 \times 0 \][/tex]
[tex]\[ 0 = 0 \][/tex]
This point does lie on the line.
Therefore, the point that lies on the line described by the equation [tex]\( y + 3 = 2(x - 1) \)[/tex] is:
F. (1, -3)
A. (2, 1)
B. (1, -4)
C. (0, 0)
D. (-1, -6)
E. (2, 9)
F. (1, -3)
We'll check each point one by one.
### Checking Point A: (2, 1)
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation:
[tex]\[ 1 + 3 = 2(2 - 1) \][/tex]
[tex]\[ 4 = 2 \times 1 \][/tex]
[tex]\[ 4 = 2 \][/tex]
This point does not lie on the line.
### Checking Point B: (1, -4)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -4 \)[/tex] into the equation:
[tex]\[ -4 + 3 = 2(1 - 1) \][/tex]
[tex]\[ -1 = 2 \times 0 \][/tex]
[tex]\[ -1 = 0 \][/tex]
This point does not lie on the line.
### Checking Point C: (0, 0)
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ 0 + 3 = 2(0 - 1) \][/tex]
[tex]\[ 3 = 2 \times -1 \][/tex]
[tex]\[ 3 = -2 \][/tex]
This point does not lie on the line.
### Checking Point D: (-1, -6)
Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -6 \)[/tex] into the equation:
[tex]\[ -6 + 3 = 2(-1 - 1) \][/tex]
[tex]\[ -3 = 2 \times -2 \][/tex]
[tex]\[ -3 = -4 \][/tex]
This point does not lie on the line.
### Checking Point E: (2, 9)
Substitute [tex]\( x = 2 \)[/tex] and [tex]\( y = 9 \)[/tex] into the equation:
[tex]\[ 9 + 3 = 2(2 - 1) \][/tex]
[tex]\[ 12 = 2 \times 1 \][/tex]
[tex]\[ 12 = 2 \][/tex]
This point does not lie on the line.
### Checking Point F: (1, -3)
Substitute [tex]\( x = 1 \)[/tex] and [tex]\( y = -3 \)[/tex] into the equation:
[tex]\[ -3 + 3 = 2(1 - 1) \][/tex]
[tex]\[ 0 = 2 \times 0 \][/tex]
[tex]\[ 0 = 0 \][/tex]
This point does lie on the line.
Therefore, the point that lies on the line described by the equation [tex]\( y + 3 = 2(x - 1) \)[/tex] is:
F. (1, -3)
