Which set of points are on the line y=6x-6
1.{(0,-6),(12,3)}
2.{(0,-6),(3,12)}
3.{(-6,0),(12,3)}
4.{(6,0),(3,12)}
Plug in the value of x and y of each point in the equation of the line. If it satisfies, then that point is a solution or is located on the line.
For instance, take (0,-6). In this point, x = 0 and y = -6. If you substitute x = 0 to the equation, you should get a value of y = -6:
y = 6x - 6
y = 6(0) - 6
y = 0 - 6
y = -6
Thus (0,-6) is a point on the line.
Try doing the others.
Put x and y values into equation : y = 6 x - 6
1.
x = 0 , y = - 6
y = 6 x - 6
y = 6 * 0 - 6 = 0 - 6 = - 6
Correct
x = 12 , y = 3
y = 6 x - 6
y = 6 * 12 - 6 = 72 - 6 = - 66
Not correct
One correct set and one uncorrect set.
So ansver 1 is not correct.
2.
x = 0 , y = - 6
y = 6 x - 6
y = 6 * 0 - 6 = 0 - 6 = - 6
Correct
x = 3 , y = 12
y = 6 x - 6
y = 6 * 3 - 6 = 18 - 6 = 12
Correct
So ansver 2 is correct.
3.
x = - 6 , y = 0
y = 6 x - 6
y = 6 * - 6 - 6 = - 36 - 6 = - - 42
Not correct
x = 12 , y = 3
y = 6 x - 6
y = 6 * 12 - 6 = 72 - 6 = 66
Not correct
So ansver 3 is not correct.
4.
x = 6 , y = 0
y = 6 x - 6
y = 6 * 6 - 6 = 36 - 6 = - 30
Not correct
x = 3 , y = 12
y = 6 x - 6
y = 6 * 13 - 6 = 78 - 6 = 72
Not correct
So ansver 4 is not correct.
Answer 2
To determine which set of points are on the line y = 6x - 6, we need to substitute the x and y values of each point into the equation and check if the equation holds true.
Let's check each set of points one by one:
1. {(0, -6), (12, 3)}
For the point (0, -6):
y = 6x - 6
-6 = 6(0) - 6
-6 = -6
The equation holds true for the point (0, -6).
For the point (12, 3):
y = 6x - 6
3 = 6(12) - 6
3 = 72 - 6
3 = 66
The equation does not hold true for the point (12, 3).
Therefore, this set {(0, -6), (12, 3)} is not on the line y = 6x - 6.
2. {(0, -6), (3, 12)}
For the point (0, -6):
y = 6x - 6
-6 = 6(0) - 6
-6 = -6
The equation holds true for the point (0, -6).
For the point (3, 12):
y = 6x - 6
12 = 6(3) - 6
12 = 18 - 6
12 = 12
The equation holds true for the point (3, 12).
Therefore, this set {(0, -6), (3, 12)} is on the line y = 6x - 6.
3. {(-6, 0), (12, 3)}
For the point (-6, 0):
y = 6x - 6
0 = 6(-6) - 6
0 = -36 - 6
0 = -42
The equation does not hold true for the point (-6, 0).
For the point (12, 3):
y = 6x - 6
3 = 6(12) - 6
3 = 72 - 6
3 = 66
The equation does not hold true for the point (12, 3).
Therefore, this set {(-6, 0), (12, 3)} is not on the line y = 6x - 6.
4. {(6, 0), (3, 12)}
For the point (6, 0):
y = 6x - 6
0 = 6(6) - 6
0 = 36 - 6
0 = 30
The equation does not hold true for the point (6, 0).
For the point (3, 12):
y = 6x - 6
12 = 6(3) - 6
12 = 18 - 6
12 = 12
The equation holds true for the point (3, 12).
Therefore, this set {(6, 0), (3, 12)} is not on the line y = 6x - 6.
Based on our analysis, only the set {(0, -6), (3, 12)} is on the line y = 6x - 6. So, the correct option is 2.