Answer :
To determine which points lie on the line described by the equation [tex]\( y = 5x \)[/tex], we need to check each point individually by substituting the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values into the equation and verifying if the equation holds true.
Let's check each point one by one:
Point A: [tex]\((3, 6)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 6 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 3 = 15 \][/tex]
The given [tex]\( y \)[/tex] value is 6, so [tex]\( 6 \neq 15 \)[/tex]. This point is not on the line.
Point B: [tex]\((3, 15)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 15 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 3 = 15 \][/tex]
The given [tex]\( y \)[/tex] value is 15, so [tex]\( 15 = 15 \)[/tex]. This point is on the line.
Point C: [tex]\((-1, -5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -5 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot (-1) = -5 \][/tex]
The given [tex]\( y \)[/tex] value is -5, so [tex]\( -5 = -5 \)[/tex]. This point is on the line.
Point D: [tex]\((0, 1)\)[/tex]
- Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 0 = 0 \][/tex]
The given [tex]\( y \)[/tex] value is 1, so [tex]\( 1 \neq 0 \)[/tex]. This point is not on the line.
Point E: [tex]\((4, 2)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 4 = 20 \][/tex]
The given [tex]\( y \)[/tex] value is 2, so [tex]\( 2 \neq 20 \)[/tex]. This point is not on the line.
Point F: [tex]\((-1, 5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 5 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot (-1) = -5 \][/tex]
The given [tex]\( y \)[/tex] value is 5, so [tex]\( 5 \neq -5 \)[/tex]. This point is not on the line.
To summarize, the points that lie on the line described by the equation [tex]\( y = 5x \)[/tex] are:
- B. [tex]\((3, 15)\)[/tex]
- C. [tex]\((-1, -5)\)[/tex]
Let's check each point one by one:
Point A: [tex]\((3, 6)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 6 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 3 = 15 \][/tex]
The given [tex]\( y \)[/tex] value is 6, so [tex]\( 6 \neq 15 \)[/tex]. This point is not on the line.
Point B: [tex]\((3, 15)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 15 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 3 = 15 \][/tex]
The given [tex]\( y \)[/tex] value is 15, so [tex]\( 15 = 15 \)[/tex]. This point is on the line.
Point C: [tex]\((-1, -5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = -5 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot (-1) = -5 \][/tex]
The given [tex]\( y \)[/tex] value is -5, so [tex]\( -5 = -5 \)[/tex]. This point is on the line.
Point D: [tex]\((0, 1)\)[/tex]
- Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 1 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 0 = 0 \][/tex]
The given [tex]\( y \)[/tex] value is 1, so [tex]\( 1 \neq 0 \)[/tex]. This point is not on the line.
Point E: [tex]\((4, 2)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] and [tex]\( y = 2 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot 4 = 20 \][/tex]
The given [tex]\( y \)[/tex] value is 2, so [tex]\( 2 \neq 20 \)[/tex]. This point is not on the line.
Point F: [tex]\((-1, 5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] and [tex]\( y = 5 \)[/tex] into the equation [tex]\( y = 5x \)[/tex]:
[tex]\[ y = 5 \cdot (-1) = -5 \][/tex]
The given [tex]\( y \)[/tex] value is 5, so [tex]\( 5 \neq -5 \)[/tex]. This point is not on the line.
To summarize, the points that lie on the line described by the equation [tex]\( y = 5x \)[/tex] are:
- B. [tex]\((3, 15)\)[/tex]
- C. [tex]\((-1, -5)\)[/tex]
