Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To determine which points lie on the line given by the equation [tex]\( y = \frac{2}{3}x - 4 \)[/tex], we'll evaluate each point by substituting the [tex]\( x \)[/tex] value into the equation and checking if the [tex]\( y \)[/tex] value matches.
Let's go through each point one-by-one:
1. Point [tex]\((6,0)\)[/tex]:
Substitute [tex]\( x = 6 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(6) - 4 = 4 - 4 = 0 \][/tex]
Since [tex]\( y = 0 \)[/tex], the point [tex]\((6, 0)\)[/tex] lies on the line.
2. Point [tex]\((-3, -6)\)[/tex]:
Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(-3) - 4 = -2 - 4 = -6 \][/tex]
Since [tex]\( y = -6 \)[/tex], the point [tex]\((-3, -6)\)[/tex] lies on the line.
3. Point [tex]\((0, 4)\)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(0) - 4 = 0 - 4 = -4 \][/tex]
Since [tex]\( y \neq 4 \)[/tex], the point [tex]\((0, 4)\)[/tex] does not lie on the line.
4. Point [tex]\((-2, -3)\)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(-2) - 4 = -\frac{4}{3} - 4 \approx -5.33 \][/tex]
Since [tex]\( y \approx -5.33 \)[/tex], the point [tex]\((-2, -3)\)[/tex] does not lie on the line.
5. Point [tex]\((0, -4)\)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(0) - 4 = 0 - 4 = -4 \][/tex]
Since [tex]\( y = -4 \)[/tex], the point [tex]\((0, -4)\)[/tex] lies on the line.
6. Point [tex]\((4, 0)\)[/tex]:
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(4) - 4 = \frac{8}{3} - 4 = \frac{8}{3} - \frac{12}{3} = -\frac{4}{3} \][/tex]
Since [tex]\( y \neq 0 \)[/tex], the point [tex]\((4, 0)\)[/tex] does not lie on the line.
7. Point [tex]\((5, 2)\)[/tex]:
Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(5) - 4 = \frac{10}{3} - 4 = \frac{10}{3} - \frac{12}{3} = -\frac{2}{3} \][/tex]
Since [tex]\( y \neq 2 \)[/tex], the point [tex]\((5, 2)\)[/tex] does not lie on the line.
8. Point [tex]\((3, -2)\)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(3) - 4 = 2 - 4 = -2 \][/tex]
Since [tex]\( y = -2 \)[/tex], the point [tex]\((3, -2)\)[/tex] lies on the line.
So, the points that the line [tex]\( y = \frac{2}{3}x - 4 \)[/tex] goes through are:
- [tex]\((6, 0)\)[/tex]
- [tex]\((-3, -6)\)[/tex]
- [tex]\((0, -4)\)[/tex]
- [tex]\((3, -2)\)[/tex]
Let's go through each point one-by-one:
1. Point [tex]\((6,0)\)[/tex]:
Substitute [tex]\( x = 6 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(6) - 4 = 4 - 4 = 0 \][/tex]
Since [tex]\( y = 0 \)[/tex], the point [tex]\((6, 0)\)[/tex] lies on the line.
2. Point [tex]\((-3, -6)\)[/tex]:
Substitute [tex]\( x = -3 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(-3) - 4 = -2 - 4 = -6 \][/tex]
Since [tex]\( y = -6 \)[/tex], the point [tex]\((-3, -6)\)[/tex] lies on the line.
3. Point [tex]\((0, 4)\)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(0) - 4 = 0 - 4 = -4 \][/tex]
Since [tex]\( y \neq 4 \)[/tex], the point [tex]\((0, 4)\)[/tex] does not lie on the line.
4. Point [tex]\((-2, -3)\)[/tex]:
Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(-2) - 4 = -\frac{4}{3} - 4 \approx -5.33 \][/tex]
Since [tex]\( y \approx -5.33 \)[/tex], the point [tex]\((-2, -3)\)[/tex] does not lie on the line.
5. Point [tex]\((0, -4)\)[/tex]:
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(0) - 4 = 0 - 4 = -4 \][/tex]
Since [tex]\( y = -4 \)[/tex], the point [tex]\((0, -4)\)[/tex] lies on the line.
6. Point [tex]\((4, 0)\)[/tex]:
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(4) - 4 = \frac{8}{3} - 4 = \frac{8}{3} - \frac{12}{3} = -\frac{4}{3} \][/tex]
Since [tex]\( y \neq 0 \)[/tex], the point [tex]\((4, 0)\)[/tex] does not lie on the line.
7. Point [tex]\((5, 2)\)[/tex]:
Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(5) - 4 = \frac{10}{3} - 4 = \frac{10}{3} - \frac{12}{3} = -\frac{2}{3} \][/tex]
Since [tex]\( y \neq 2 \)[/tex], the point [tex]\((5, 2)\)[/tex] does not lie on the line.
8. Point [tex]\((3, -2)\)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[ y = \frac{2}{3}(3) - 4 = 2 - 4 = -2 \][/tex]
Since [tex]\( y = -2 \)[/tex], the point [tex]\((3, -2)\)[/tex] lies on the line.
So, the points that the line [tex]\( y = \frac{2}{3}x - 4 \)[/tex] goes through are:
- [tex]\((6, 0)\)[/tex]
- [tex]\((-3, -6)\)[/tex]
- [tex]\((0, -4)\)[/tex]
- [tex]\((3, -2)\)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.