which piont lies on the line defined by 3x+6y=2?
a (0,2)
b (o,6)
c {1,-1/6}
d {1,-1/3}
c)
3x + 6y = 2
at (1, -1/6)
3(1) + 6(-1/6) = 2
3 - 1 = 2
true, so the point (1,-1/6) lies on the line
Well, let me analyze this for you. We can find the point that lies on the line by substituting the given x and y values in the equation 3x + 6y = 2 to see if it holds true. Let's check each option:
a) (0,2): 3(0) + 6(2) = 12 ≠ 2. So, (0,2) does not lie on the line.
b) (0,6): 3(0) + 6(6) = 36 ≠ 2. So, (0,6) does not lie on the line.
c) (1, -1/6): 3(1) + 6(-1/6) = 3 - 1 = 2. Voila! (1, -1/6) satisfies the equation and lies on the line.
d) (1, -1/3): 3(1) + 6(-1/3) = 3 - 2 = 1 ≠ 2. So, (1, -1/3) does not lie on the line.
Therefore, the answer is c) (1, -1/6). It's quite the point to "line" up with, don't you think?
To determine which point lies on the line defined by the equation 3x + 6y = 2, you can substitute the x and y values of each point into the equation and check if it satisfies the equation.
Let's check each point:
a) (0,2):
Substituting x = 0 and y = 2 into the equation:
3(0) + 6(2) = 2
0 + 12 = 2
12 does not equal 2, so point (0,2) does not lie on the line.
b) (0,6):
Substituting x = 0 and y = 6 into the equation:
3(0) + 6(6) = 2
0 + 36 = 2
36 does not equal 2, so point (0,6) does not lie on the line.
c) (1, -1/6):
Substituting x = 1 and y = -1/6 into the equation:
3(1) + 6(-1/6) = 2
3 - 1 = 2
2 does not equal 2, so point (1, -1/6) does not lie on the line.
d) (1, -1/3):
Substituting x = 1 and y = -1/3 into the equation:
3(1) + 6(-1/3) = 2
3 - 2 = 2
1 does not equal 2, so point (1, -1/3) does not lie on the line.
Therefore, none of the given points (a, b, c, or d) lie on the line defined by the equation 3x + 6y = 2.
To determine which point lies on the line defined by the equation 3x + 6y = 2, we need to substitute the given points into the equation and see if they satisfy it.
Let's check each point:
a) (0,2)
Substitute x = 0 and y = 2 into the equation:
3(0) + 6(2) = 2
0 + 12 = 2
This is not true, so point a (0,2) does not lie on the line.
b) (0,6)
Substitute x = 0 and y = 6 into the equation:
3(0) + 6(6) = 2
0 + 36 = 2
This is not true, so point b (0,6) does not lie on the line.
c) (1,-1/6)
Substitute x = 1 and y = -1/6 into the equation:
3(1) + 6(-1/6) = 2
3 - 1 = 2
2 = 2
This is true, so point c (1, -1/6) lies on the line.
d) (1,-1/3)
Substitute x = 1 and y = -1/3 into the equation:
3(1) + 6(-1/3) = 2
3 - 2 = 2
1 = 2
This is not true, so point d (1, -1/3) does not lie on the line.
Therefore, the point that lies on the line defined by 3x + 6y = 2 is c) (1, -1/6).