To determine which points lie on the line given by the equation [tex]\( y = 5x \)[/tex], we need to check if the coordinates of each point satisfy the equation. We will do this point by point:
Point A: (4, 2)
- Substitute [tex]\( x = 4 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot 4 = 20 \)[/tex].
- Since [tex]\( 2 \neq 20 \)[/tex], the point [tex]\( (4, 2) \)[/tex] does not lie on the line.
Point B: (-1, 5)
- Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot (-1) = -5 \)[/tex].
- Since [tex]\( 5 \neq -5 \)[/tex], the point [tex]\( (-1, 5) \)[/tex] does not lie on the line.
Point C: (3, 6)
- Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot 3 = 15 \)[/tex].
- Since [tex]\( 6 \neq 15 \)[/tex], the point [tex]\( (3, 6) \)[/tex] does not lie on the line.
Point D: (3, 15)
- Substitute [tex]\( x = 3 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot 3 = 15 \)[/tex].
- Since [tex]\( 15 = 15 \)[/tex], the point [tex]\( (3, 15) \)[/tex] does lie on the line.
Point E: (0, 1)
- Substitute [tex]\( x = 0 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot 0 = 0 \)[/tex].
- Since [tex]\( 1 \neq 0 \)[/tex], the point [tex]\( (0, 1) \)[/tex] does not lie on the line.
Point F: (-1, -5)
- Substitute [tex]\( x = -1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex].
- [tex]\( y = 5 \cdot (-1) = -5 \)[/tex].
- Since [tex]\( -5 = -5 \)[/tex], the point [tex]\( (-1, -5) \)[/tex] does lie on the line.
Therefore, the points that lie on the line [tex]\( y = 5x \)[/tex] are [tex]\( D. (3, 15) \)[/tex] and [tex]\( F. (-1, -5) \)[/tex].
