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 - y1 = m(x - x1)
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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