Answer:
(-1, 3), (-2, 2) and (-5, -1) lie on the line.
Step-by-step explanation:
Let the equation of the line which is parallel to the given line is y = mx + c
Here m is the slope of line similar to the line given = (y - y')/(x - x')
Here (x, y) and (x', y') are (4, 2) and (-2, -4)
then m = (2+4)/(4+2) = 6/6 = 1
Now the equation of the line will be y = x + c
This line passes through point P(0, 4)
4 = 1×0 + c
c = 4
Therefore equation of the line will be
y = x + 4
Now we check for each point given in the question whether it lies on the line or not.
For (-4, 2)
y = (-4) + 4 = 0
Hence not lies on the line.
For (-1, 3)
y = (-1) + 4 = -1 +4 = 3
Hence (-1,3) lies on the line.
For (-2, 2)
y = (-2) + 4 = -2 + 4 = 2
Hence (-2, 2) lies on the line.
For (4, 2)
y = 4 + 4 = 8
Hence (4, 2) lies on the line.
For (-5, -1)
y = -5 + 4 = -1
Hence (-5, -1) lies on the line.
Therefore (-1, 3),(-2, 2) and (-5, -1) lie on the line.
