To determine which of the given points lie on the line defined by the equation [tex]\( y = 2x \)[/tex], we need to check each point to see if it satisfies the equation. We will substitute the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] coordinates of each point into the equation and verify if both sides of the equation are equal.
The equation is [tex]\( y = 2x \)[/tex].
Let's check each point one by one.
Point A: [tex]\((3, 6)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation: [tex]\( y = 2(3) \)[/tex]
- This gives [tex]\( y = 6 \)[/tex]
- The coordinates [tex]\((3, 6)\)[/tex] satisfy the equation, so this point is on the line.
Point B: [tex]\((5, 10)\)[/tex]
- Substitute [tex]\( x = 5 \)[/tex] into the equation: [tex]\( y = 2(5) \)[/tex]
- This gives [tex]\( y = 10 \)[/tex]
- The coordinates [tex]\((5, 10)\)[/tex] satisfy the equation, so this point is on the line.
Point C: [tex]\((1, 3)\)[/tex]
- Substitute [tex]\( x = 1 \)[/tex] into the equation: [tex]\( y = 2(1) \)[/tex]
- This gives [tex]\( y = 2 \)[/tex]
- The coordinates [tex]\((1, 3)\)[/tex] do not satisfy the equation, so this point is not on the line.
Point D: [tex]\((4, 6)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] into the equation: [tex]\( y = 2(4) \)[/tex]
- This gives [tex]\( y = 8 \)[/tex]
- The coordinates [tex]\((4, 6)\)[/tex] do not satisfy the equation, so this point is not on the line.
Point E: [tex]\((16, 8)\)[/tex]
- Substitute [tex]\( x = 16 \)[/tex] into the equation: [tex]\( y = 2(16) \)[/tex]
- This gives [tex]\( y = 32 \)[/tex]
- The coordinates [tex]\((16, 8)\)[/tex] do not satisfy the equation, so this point is not on the line.
Point F: [tex]\((4, 2)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] into the equation: [tex]\( y = 2(4) \)[/tex]
- This gives [tex]\( y = 8 \)[/tex]
- The coordinates [tex]\((4, 2)\)[/tex] do not satisfy the equation, so this point is not on the line.
After checking all the points, the ones that satisfy the equation [tex]\( y = 2x \)[/tex] and hence lie on the line are:
- [tex]\((3, 6)\)[/tex]
- [tex]\((5, 10)\)[/tex]
So, the points that are on the line [tex]\( y = 2x \)[/tex] are:
[tex]\[ \boxed{A. (3, 6) \text{ and } B. (5, 10)} \][/tex]
