To determine which of the given points lie on the line defined by the equation [tex]\( y = 5x \)[/tex], we need to check each point individually. We do this by substituting the [tex]\( x \)[/tex]-value of each point into the equation and seeing if the resulting [tex]\( y \)[/tex]-value matches the [tex]\( y \)[/tex]-coordinate of the point.
Let's go through each point one by one:
1. Point A: [tex]\( (-1, -5) \)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(-1) = -5 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(-5\)[/tex], which matches the [tex]\( y \)[/tex]-coordinate of the point [tex]\((-1, -5)\)[/tex].
- Therefore, point A lies on the line.
2. Point B: [tex]\( (0, 1) \)[/tex]
- Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(0) = 0 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(0\)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\( (0, 1) \)[/tex].
- Therefore, point B does not lie on the line.
3. Point C: [tex]\( (3, 15) \)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(3) = 15 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(15\)[/tex], which matches the [tex]\( y \)[/tex]-coordinate of the point [tex]\( (3, 15) \)[/tex].
- Therefore, point C lies on the line.
4. Point D: [tex]\( (-1, 5) \)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(-1) = -5 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(-5\)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\( (-1, 5) \)[/tex].
- Therefore, point D does not lie on the line.
5. Point E: [tex]\( (4, 2) \)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(4) = 20 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(20\)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\( (4, 2) \)[/tex].
- Therefore, point E does not lie on the line.
6. Point F: [tex]\( (3, 6) \)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5(3) = 15 \)[/tex].
- The [tex]\( y \)[/tex]-value obtained is [tex]\(15\)[/tex], which does not match the [tex]\( y \)[/tex]-coordinate of the point [tex]\( (3, 6) \)[/tex].
- Therefore, point F does not lie on the line.
Given the above calculations, the points that lie on the line [tex]\( y = 5x \)[/tex] are:
- A. [tex]\( (-1, -5) \)[/tex]
- C. [tex]\( (3, 15) \)[/tex]
