Question
which of these points lies on the line described by the equation below y-5=6(x-7)
Answers
GPT 3.5
To determine which point lies on the line described by the equation, we can substitute the coordinates of each point into the equation and see if the equation holds true.
Let's test each point:
Point A: (7, 5)
Substituting the values into the equation:
5 - 5 = 6(7 - 7)
0 = 6(0)
0 = 0
The equation holds true for this point, so (7, 5) lies on the line.
Point B: (2, -7)
Substituting the values into the equation:
-7 - 5 = 6(2 - 7)
-12 = 6(-5)
-12 = -30
The equation does not hold true for this point, so (2, -7) does not lie on the line.
Point C: (-1, -11)
Substituting the values into the equation:
-11 - 5 = 6(-1 - 7)
-16 = 6(-8)
-16 = -48
The equation does not hold true for this point, so (-1, -11) does not lie on the line.
Point D: (10, 11)
Substituting the values into the equation:
11 - 5 = 6(10 - 7)
6 = 6(3)
6 = 18
The equation does not hold true for this point, so (10, 11) does not lie on the line.
Therefore, the only point that lies on the line described by the equation y - 5 = 6(x - 7) is Point A: (7, 5).
Let's test each point:
Point A: (7, 5)
Substituting the values into the equation:
5 - 5 = 6(7 - 7)
0 = 6(0)
0 = 0
The equation holds true for this point, so (7, 5) lies on the line.
Point B: (2, -7)
Substituting the values into the equation:
-7 - 5 = 6(2 - 7)
-12 = 6(-5)
-12 = -30
The equation does not hold true for this point, so (2, -7) does not lie on the line.
Point C: (-1, -11)
Substituting the values into the equation:
-11 - 5 = 6(-1 - 7)
-16 = 6(-8)
-16 = -48
The equation does not hold true for this point, so (-1, -11) does not lie on the line.
Point D: (10, 11)
Substituting the values into the equation:
11 - 5 = 6(10 - 7)
6 = 6(3)
6 = 18
The equation does not hold true for this point, so (10, 11) does not lie on the line.
Therefore, the only point that lies on the line described by the equation y - 5 = 6(x - 7) is Point A: (7, 5).
which is not an equation of the line going through (6,7)and (2,-1)
y-1=2(x+2)
y-7=2(x-6)
y=2x-5
y+1=2(x-2)
y-1=2(x+2)
y-7=2(x-6)
y=2x-5
y+1=2(x-2)
GPT 3.5
To determine which equation is not of the line going through (6,7) and (2,-1), we can substitute the coordinates of each point into each equation and see if the equation holds true.
Let's test each equation:
Equation 1: y - 1 = 2(x + 2)
Substituting (6,7):
7 - 1 = 2(6 + 2)
6 = 2(8)
6 = 16
The equation does not hold true for this point.
Equation 2: y - 7 = 2(x - 6)
Substituting (6,7):
7 - 7 = 2(6 - 6)
0 = 2(0)
0 = 0
The equation holds true for this point.
Equation 3: y = 2x - 5
Substituting (6,7):
7 = 2(6) - 5
7 = 12 - 5
7 = 7
The equation holds true for this point.
Equation 4: y + 1 = 2(x - 2)
Substituting (6,7):
7 + 1 = 2(6 - 2)
8 = 2(4)
8 = 8
The equation holds true for this point.
Therefore, the equation that is not of the line going through (6,7) and (2,-1) is Equation 1: y - 1 = 2(x + 2).
Let's test each equation:
Equation 1: y - 1 = 2(x + 2)
Substituting (6,7):
7 - 1 = 2(6 + 2)
6 = 2(8)
6 = 16
The equation does not hold true for this point.
Equation 2: y - 7 = 2(x - 6)
Substituting (6,7):
7 - 7 = 2(6 - 6)
0 = 2(0)
0 = 0
The equation holds true for this point.
Equation 3: y = 2x - 5
Substituting (6,7):
7 = 2(6) - 5
7 = 12 - 5
7 = 7
The equation holds true for this point.
Equation 4: y + 1 = 2(x - 2)
Substituting (6,7):
7 + 1 = 2(6 - 2)
8 = 2(4)
8 = 8
The equation holds true for this point.
Therefore, the equation that is not of the line going through (6,7) and (2,-1) is Equation 1: y - 1 = 2(x + 2).