Answer :
Let's analyze if the point [tex]\((4, 1)\)[/tex] satisfies the equation [tex]\(y = 6x\)[/tex].
1. Identify the given point and equation:
- Point: [tex]\( (4, 1) \)[/tex]
- Equation: [tex]\( y = 6x \)[/tex]
2. Substitute the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates of the point into the equation:
- The coordinates of the point are [tex]\( x = 4 \)[/tex] and [tex]\( y = 1 \)[/tex].
3. Evaluate the right-hand side of the equation using the given [tex]\(x\)[/tex]-coordinate:
- Substitute [tex]\(x = 4\)[/tex] into the equation [tex]\(y = 6x\)[/tex]:
[tex]\[ y = 6 \cdot 4 \][/tex]
[tex]\[ y = 24 \][/tex]
4. Compare the evaluated right-hand side with the given [tex]\(y\)[/tex]-coordinate:
- The left-hand side gives the [tex]\(y\)[/tex]-value from the point, which is [tex]\(y = 1\)[/tex].
- The right-hand side, based on our substitution, gives [tex]\(y = 24\)[/tex].
5. Check for equality:
- Compare [tex]\(1\)[/tex] (the left-hand side) with [tex]\(24\)[/tex] (the right-hand side):
[tex]\[ 1 \neq 24 \][/tex]
Since the left-hand side does not equal the right-hand side, the point [tex]\((4, 1)\)[/tex] does not satisfy the equation [tex]\(y = 6x\)[/tex].
Therefore, the correct answer is:
No
1. Identify the given point and equation:
- Point: [tex]\( (4, 1) \)[/tex]
- Equation: [tex]\( y = 6x \)[/tex]
2. Substitute the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates of the point into the equation:
- The coordinates of the point are [tex]\( x = 4 \)[/tex] and [tex]\( y = 1 \)[/tex].
3. Evaluate the right-hand side of the equation using the given [tex]\(x\)[/tex]-coordinate:
- Substitute [tex]\(x = 4\)[/tex] into the equation [tex]\(y = 6x\)[/tex]:
[tex]\[ y = 6 \cdot 4 \][/tex]
[tex]\[ y = 24 \][/tex]
4. Compare the evaluated right-hand side with the given [tex]\(y\)[/tex]-coordinate:
- The left-hand side gives the [tex]\(y\)[/tex]-value from the point, which is [tex]\(y = 1\)[/tex].
- The right-hand side, based on our substitution, gives [tex]\(y = 24\)[/tex].
5. Check for equality:
- Compare [tex]\(1\)[/tex] (the left-hand side) with [tex]\(24\)[/tex] (the right-hand side):
[tex]\[ 1 \neq 24 \][/tex]
Since the left-hand side does not equal the right-hand side, the point [tex]\((4, 1)\)[/tex] does not satisfy the equation [tex]\(y = 6x\)[/tex].
Therefore, the correct answer is:
No
