Answer :
To determine which point lies on the line described by the equation [tex]\( y + 3 = 2(x - 1) \)[/tex], we need to test each point by substituting the coordinates [tex]\( (x, y) \)[/tex] into the equation and verifying if the equation holds true. Let’s simplify the line equation first:
[tex]\[ y + 3 = 2(x - 1) \][/tex]
Rewriting it in the standard form [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex]:
[tex]\[ y + 3 = 2x - 2 \][/tex]
Subtracting 3 from both sides, we get:
[tex]\[ y = 2x - 5 \][/tex]
Now we will test each point:
A. (1, -3)
[tex]\[ y = 2(1) - 5 \][/tex]
[tex]\[ -3 = 2 - 5 \][/tex]
[tex]\[ -3 = -3 \quad \text{(True)} \][/tex]
B. (0, 0)
[tex]\[ y = 2(0) - 5 \][/tex]
[tex]\[ 0 = -5 \quad \text{(False)} \][/tex]
C. (-1, -6)
[tex]\[ y = 2(-1) - 5 \][/tex]
[tex]\[ -6 = -2 - 5 \][/tex]
[tex]\[ -6 = -7 \quad \text{(False)} \][/tex]
D. (2, 1)
[tex]\[ y = 2(2) - 5 \][/tex]
[tex]\[ 1 = 4 - 5 \][/tex]
[tex]\[ 1 = -1 \quad \text{(False)} \][/tex]
E. (1, -4)
[tex]\[ y = 2(1) - 5 \][/tex]
[tex]\[ -4 = 2 - 5 \][/tex]
[tex]\[ -4 = -3 \quad \text{(False)} \][/tex]
F. (2, 9)
[tex]\[ y = 2(2) - 5 \][/tex]
[tex]\[ 9 = 4 - 5 \][/tex]
[tex]\[ 9 = -1 \quad \text{(False)} \][/tex]
From the calculations, the only point that satisfies the equation [tex]\( y + 3 = 2(x - 1) \)[/tex] is:
A. (1, -3)
Therefore, the point [tex]\( (1, -3) \)[/tex] lies on the line described by the equation.
[tex]\[ y + 3 = 2(x - 1) \][/tex]
Rewriting it in the standard form [tex]\( y \)[/tex] as a function of [tex]\( x \)[/tex]:
[tex]\[ y + 3 = 2x - 2 \][/tex]
Subtracting 3 from both sides, we get:
[tex]\[ y = 2x - 5 \][/tex]
Now we will test each point:
A. (1, -3)
[tex]\[ y = 2(1) - 5 \][/tex]
[tex]\[ -3 = 2 - 5 \][/tex]
[tex]\[ -3 = -3 \quad \text{(True)} \][/tex]
B. (0, 0)
[tex]\[ y = 2(0) - 5 \][/tex]
[tex]\[ 0 = -5 \quad \text{(False)} \][/tex]
C. (-1, -6)
[tex]\[ y = 2(-1) - 5 \][/tex]
[tex]\[ -6 = -2 - 5 \][/tex]
[tex]\[ -6 = -7 \quad \text{(False)} \][/tex]
D. (2, 1)
[tex]\[ y = 2(2) - 5 \][/tex]
[tex]\[ 1 = 4 - 5 \][/tex]
[tex]\[ 1 = -1 \quad \text{(False)} \][/tex]
E. (1, -4)
[tex]\[ y = 2(1) - 5 \][/tex]
[tex]\[ -4 = 2 - 5 \][/tex]
[tex]\[ -4 = -3 \quad \text{(False)} \][/tex]
F. (2, 9)
[tex]\[ y = 2(2) - 5 \][/tex]
[tex]\[ 9 = 4 - 5 \][/tex]
[tex]\[ 9 = -1 \quad \text{(False)} \][/tex]
From the calculations, the only point that satisfies the equation [tex]\( y + 3 = 2(x - 1) \)[/tex] is:
A. (1, -3)
Therefore, the point [tex]\( (1, -3) \)[/tex] lies on the line described by the equation.
