Answer :
To determine which of the given points lie on the line described by the equation [tex]\( y = 5x \)[/tex], we need to check if each point satisfies this equation. Here are the steps to do so:
1. Point A: [tex]\((-1, 5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(-1) = -5 \)[/tex]
- The point A is [tex]\( (-1, 5) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(-5\)[/tex]
- Since [tex]\( 5 \neq -5 \)[/tex], point A is not on the line.
2. Point B: [tex]\((-1, -5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(-1) = -5 \)[/tex]
- The point B is [tex]\( (-1, -5) \)[/tex], which matches [tex]\( y = -5 \)[/tex]
- Therefore, point B is on the line.
3. Point C: [tex]\((0, 1)\)[/tex]
- Substitute [tex]\( x = 0 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(0) = 0 \)[/tex]
- The point C is [tex]\( (0, 1) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(0\)[/tex]
- Since [tex]\( 1 \neq 0 \)[/tex], point C is not on the line.
4. Point D: [tex]\((4, 2)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(4) = 20 \)[/tex]
- The point D is [tex]\( (4, 2) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(20\)[/tex]
- Since [tex]\( 2 \neq 20 \)[/tex], point D is not on the line.
5. Point E: [tex]\((3, 6)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(3) = 15 \)[/tex]
- The point E is [tex]\( (3, 6) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(15\)[/tex]
- Since [tex]\( 6 \neq 15 \)[/tex], point E is not on the line.
6. Point F: [tex]\((3, 15)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(3) = 15 \)[/tex]
- The point F is [tex]\( (3, 15) \)[/tex], which matches [tex]\( y = 15 \)[/tex]
- Therefore, point F is on the line.
Based on this analysis, the points that lie on the line [tex]\( y = 5x \)[/tex] are:
- B: [tex]\((-1, -5)\)[/tex]
- F: [tex]\((3, 15)\)[/tex]
1. Point A: [tex]\((-1, 5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(-1) = -5 \)[/tex]
- The point A is [tex]\( (-1, 5) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(-5\)[/tex]
- Since [tex]\( 5 \neq -5 \)[/tex], point A is not on the line.
2. Point B: [tex]\((-1, -5)\)[/tex]
- Substitute [tex]\( x = -1 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(-1) = -5 \)[/tex]
- The point B is [tex]\( (-1, -5) \)[/tex], which matches [tex]\( y = -5 \)[/tex]
- Therefore, point B is on the line.
3. Point C: [tex]\((0, 1)\)[/tex]
- Substitute [tex]\( x = 0 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(0) = 0 \)[/tex]
- The point C is [tex]\( (0, 1) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(0\)[/tex]
- Since [tex]\( 1 \neq 0 \)[/tex], point C is not on the line.
4. Point D: [tex]\((4, 2)\)[/tex]
- Substitute [tex]\( x = 4 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(4) = 20 \)[/tex]
- The point D is [tex]\( (4, 2) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(20\)[/tex]
- Since [tex]\( 2 \neq 20 \)[/tex], point D is not on the line.
5. Point E: [tex]\((3, 6)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(3) = 15 \)[/tex]
- The point E is [tex]\( (3, 6) \)[/tex], hence the [tex]\( y \)[/tex]-value should be [tex]\(15\)[/tex]
- Since [tex]\( 6 \neq 15 \)[/tex], point E is not on the line.
6. Point F: [tex]\((3, 15)\)[/tex]
- Substitute [tex]\( x = 3 \)[/tex] into the equation: [tex]\( y = 5x \)[/tex]
- Calculate: [tex]\( y = 5(3) = 15 \)[/tex]
- The point F is [tex]\( (3, 15) \)[/tex], which matches [tex]\( y = 15 \)[/tex]
- Therefore, point F is on the line.
Based on this analysis, the points that lie on the line [tex]\( y = 5x \)[/tex] are:
- B: [tex]\((-1, -5)\)[/tex]
- F: [tex]\((3, 15)\)[/tex]
