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# Which point is on the line that passes through (0, 6) and is parallel to the given line with slope -1/6?

(-12, 8), (-6, 6), (2, 8), (6, 0)

**Solution:**

It is given that

Slope of line = -1/6

The line passes through (0, 6)

Let us make use of the point slope formula

y - y_{1} = m(x - x_{1})

Substituting the values

y - 6 = -1/6 (x - 0)

y - 6 = -x/6

y + x/6 = 6

Taking LCM

6y + x = 36

x + 6y = 36

To find the point which lies on the line, put the values of x and y in equation

From the options above,

1) Point (-12, 8)

x + 6y = 36

-12 + 6(8) = 36

-12 + 48 = 36

36 = 36

LHS = RHS

Therefore, the point (-12, 8) lies on the line.

2) Point (6, 0)

x + 6y = 36

6 + 6(0) = 36

6 ≠ 36

LHS ≠ RHS

Therefore, the point (6,0) does not lie on the line.

3) point (-6,6)

x + 6y = 36

-6 + 6(6) = 36

-6 + 36 = 36

30 ≠ 36

LHS ≠ RHS

Therefore, the point (-6,6) does not lie on the line.

4) point (2, 8)

x + 6y = 36

2 + 6(8) = 36

2 + 48 = 36

50 ≠ 36

LHS ≠ RHS

Hence, the point (2,8) does not lie on the line.

Therefore, the point (-12, 8) is on the line that passes through (0, 6) and is parallel to the given line.

## Which point is on the line that passes through (0, 6) and is parallel to the given line with slope -1/6?

**Summary:**

The point which is on the line that passes through (0, 6) and is parallel to the given line is (-12, 8).

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