Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which point is a solution to the inequality [tex]\( y \leq 3x - 4 \)[/tex], we need to check each point individually by substituting the [tex]\( x \)[/tex] and [tex]\( y \)[/tex] values into the inequality.
Let's examine each point:
### Point A: [tex]\((0, 4)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 4 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 4 \leq 3(0) - 4 \][/tex]
[tex]\[ 4 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 4)\)[/tex] is not a solution.
### Point B: [tex]\((3, 1)\)[/tex]
Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 1 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 1 \leq 3(3) - 4 \][/tex]
[tex]\[ 1 \leq 9 - 4 \][/tex]
[tex]\[ 1 \leq 5 \][/tex]
This is true. Therefore, [tex]\((3, 1)\)[/tex] is a solution.
### Point C: [tex]\((0, 0)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 0 \leq 3(0) - 4 \][/tex]
[tex]\[ 0 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 0)\)[/tex] is not a solution.
### Point D: [tex]\((-2, 0)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 0 \leq 3(-2) - 4 \][/tex]
[tex]\[ 0 \leq -6 - 4 \][/tex]
[tex]\[ 0 \leq -10 \][/tex]
This is not true. Therefore, [tex]\((-2, 0)\)[/tex] is not a solution.
Based on the above calculations, the point that satisfies the inequality [tex]\( y \leq 3x - 4 \)[/tex] is:
[tex]\[ \boxed{(3, 1)} \][/tex]
Let's examine each point:
### Point A: [tex]\((0, 4)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 4 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 4 \leq 3(0) - 4 \][/tex]
[tex]\[ 4 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 4)\)[/tex] is not a solution.
### Point B: [tex]\((3, 1)\)[/tex]
Substitute [tex]\( x = 3 \)[/tex] and [tex]\( y = 1 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 1 \leq 3(3) - 4 \][/tex]
[tex]\[ 1 \leq 9 - 4 \][/tex]
[tex]\[ 1 \leq 5 \][/tex]
This is true. Therefore, [tex]\((3, 1)\)[/tex] is a solution.
### Point C: [tex]\((0, 0)\)[/tex]
Substitute [tex]\( x = 0 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 0 \leq 3(0) - 4 \][/tex]
[tex]\[ 0 \leq -4 \][/tex]
This is not true. Therefore, [tex]\((0, 0)\)[/tex] is not a solution.
### Point D: [tex]\((-2, 0)\)[/tex]
Substitute [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex] into the inequality [tex]\( y \leq 3x - 4 \)[/tex]:
[tex]\[ 0 \leq 3(-2) - 4 \][/tex]
[tex]\[ 0 \leq -6 - 4 \][/tex]
[tex]\[ 0 \leq -10 \][/tex]
This is not true. Therefore, [tex]\((-2, 0)\)[/tex] is not a solution.
Based on the above calculations, the point that satisfies the inequality [tex]\( y \leq 3x - 4 \)[/tex] is:
[tex]\[ \boxed{(3, 1)} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.