Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
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)
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
