To determine which of the given points lie on the line described by the equation [tex]\( y = \frac{1}{2} x \)[/tex], we will substitute the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] coordinates of each point into the equation and see if it holds true.
1. For point [tex]\( (4,2) \)[/tex]:
- Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times 4 = 2
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value matches the given [tex]\( y \)[/tex] value, the point [tex]\( (4, 2) \)[/tex] lies on the line.
2. For point [tex]\( (-2,-1) \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times (-2) = -1
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value matches the given [tex]\( y \)[/tex] value, the point [tex]\( (-2, -1) \)[/tex] lies on the line.
3. For point [tex]\( (-2,1) \)[/tex]:
- Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times (-2) = -1
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value does not match the given [tex]\( y \)[/tex] value, the point [tex]\( (-2, 1) \)[/tex] does not lie on the line.
4. For point [tex]\( (3,15) \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times 3 = 1.5
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value does not match the given [tex]\( y \)[/tex] value, the point [tex]\( (3, 15) \)[/tex] does not lie on the line.
5. For point [tex]\( (3,6) \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times 3 = 1.5
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value does not match the given [tex]\( y \)[/tex] value, the point [tex]\( (3, 6) \)[/tex] does not lie on the line.
6. For point [tex]\( (2,1) \)[/tex]:
- Substitute [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
y = \frac{1}{2} \times 2 = 1
\][/tex]
- Since the calculated [tex]\( y \)[/tex] value matches the given [tex]\( y \)[/tex] value, the point [tex]\( (2, 1) \)[/tex] lies on the line.
Based on these calculations, the points that lie on the line [tex]\( y = \frac{1}{2} x \)[/tex] are:
- [tex]\( (4, 2) \)[/tex]
- [tex]\( (-2, -1) \)[/tex]
- [tex]\( (2, 1) \)[/tex]
Therefore, the correct points are:
A. [tex]\( (4,2) \)[/tex]
B. [tex]\( (-2,-1) \)[/tex]
F. [tex]\( (2,1) \)[/tex]
