Do the lines contain the points?

A line contains the points (0,0) and (1,4).
Select all equations that represent this line.
A.)  y = x + 4
B.)  y = 4x
C.)  (y - 0) = 4(x - 0)
D.)  x = 4y
E.)  x = 0.25y
F.)  y = 4x²

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If a point lies on a line, when the x and y values of the point are substituted into the equation, it will create a true statement such as 4 = 4 or -3 = -3.

Given points are (0,0)   →   x = 0 and y = 0
and (1,4)   →   x = 1 and y = 4

For line A.)  y = x + 4
If x = 0 and y = 0, then:
0 = 0 + 4   {substituted}
0 ≠ 4
Line A does not contain the points

For line B.)  y = 4x
If x = 0 and y = 0, then:
0 = 4(0)   {substituted}
0 = 0   {true statement}

If x = 1 and y = 4, then:
4 = 4(1)   {substituted}
4 = 4   {true statement}
Line B contains the points


For line C.)  (y - 0) = 4(x - 0)
it simplifies to y = 4x   {the same as line B.) above
Line C contains the points

For line D.)  x = 4y
If x = 0 and y = 0, then:
0 = 4(0)   {substituted}
0 = 0   {true statement}

If x = 1 and y = 4, then:
1 = 4(4)   {substituted}
1 ≠ 16
Line D does not contain the points

For line E.) x = 0.25y
If x = 0 and y = 0, then:
0 = 0.25(0)   {substituted}
0 = 0   {true statement}

If x = 1 and y = 4, then:
1 = 0.25(4)   {substituted}
1 = 1   {true statement}
Line E contains the points

For line F.)  y = 4x²
If x = 0 and y = 0, then:
0 = 4(0)²   {substituted}
0 = 0   {true statement}

If x = 1 and y = 4, then:
4 = 4(1)²   {substituted}
4 = 4   {true statement}
Line F contains the points

Equations B, C, E, and F represent this line.

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