Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine which of the given equations represents the data table, we need to check each equation against the data points provided. The data points are:
[tex]\[ (0, 3), (2, 7), (4, 11), (6, 15) \][/tex]
Let's test each equation with these points to see which one fits all the data points.
### Option A: [tex]\( y = 2x - 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) - 3 = -3 \quad \text{(This does not match \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2(2) - 3 = 4 - 3 = 1 \quad \text{(This does not match \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 2(4) - 3 = 8 - 3 = 5 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 2(6) - 3 = 12 - 3 = 9 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option A does not match the data points.
### Option B: [tex]\( y = 4x - 1 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 4(0) - 1 = -1 \quad \text{(This does not match \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 4(2) - 1 = 8 - 1 = 7 \quad \text{(This matches \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4(4) - 1 = 16 - 1 = 15 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 4(6) - 1 = 24 - 1 = 23 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option B does not match the data points.
### Option C: [tex]\( y = 2x + 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 3 = 3 \quad \text{(This matches \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2(2) + 3 = 4 + 3 = 7 \quad \text{(This matches \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 2(4) + 3 = 8 + 3 = 11 \quad \text{(This matches \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 2(6) + 3 = 12 + 3 = 15 \quad \text{(This matches \( y = 15 \))} \][/tex]
So, Option C matches all the data points.
### Option D: [tex]\( y = 4x + 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 4(0) + 3 = 3 \quad \text{(This matches \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 4(2) + 3 = 8 + 3 = 11 \quad \text{(This does not match \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4(4) + 3 = 16 + 3 = 19 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 4(6) + 3 = 24 + 3 = 27 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option D does not match the data points.
### Conclusion
The equation [tex]\( y = 2x + 3 \)[/tex] (Option C) represents the data table correctly.
[tex]\[ (0, 3), (2, 7), (4, 11), (6, 15) \][/tex]
Let's test each equation with these points to see which one fits all the data points.
### Option A: [tex]\( y = 2x - 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) - 3 = -3 \quad \text{(This does not match \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2(2) - 3 = 4 - 3 = 1 \quad \text{(This does not match \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 2(4) - 3 = 8 - 3 = 5 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 2(6) - 3 = 12 - 3 = 9 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option A does not match the data points.
### Option B: [tex]\( y = 4x - 1 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 4(0) - 1 = -1 \quad \text{(This does not match \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 4(2) - 1 = 8 - 1 = 7 \quad \text{(This matches \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4(4) - 1 = 16 - 1 = 15 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 4(6) - 1 = 24 - 1 = 23 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option B does not match the data points.
### Option C: [tex]\( y = 2x + 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 2(0) + 3 = 3 \quad \text{(This matches \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 2(2) + 3 = 4 + 3 = 7 \quad \text{(This matches \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 2(4) + 3 = 8 + 3 = 11 \quad \text{(This matches \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 2(6) + 3 = 12 + 3 = 15 \quad \text{(This matches \( y = 15 \))} \][/tex]
So, Option C matches all the data points.
### Option D: [tex]\( y = 4x + 3 \)[/tex]
1. For [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 4(0) + 3 = 3 \quad \text{(This matches \( y = 3 \))} \][/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\[ y = 4(2) + 3 = 8 + 3 = 11 \quad \text{(This does not match \( y = 7 \))} \][/tex]
3. For [tex]\( x = 4 \)[/tex]:
[tex]\[ y = 4(4) + 3 = 16 + 3 = 19 \quad \text{(This does not match \( y = 11 \))} \][/tex]
4. For [tex]\( x = 6 \)[/tex]:
[tex]\[ y = 4(6) + 3 = 24 + 3 = 27 \quad \text{(This does not match \( y = 15 \))} \][/tex]
So, Option D does not match the data points.
### Conclusion
The equation [tex]\( y = 2x + 3 \)[/tex] (Option C) represents the data table correctly.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
