IDNLearn.com connects you with experts who provide accurate and reliable answers. Discover prompt and accurate answers from our experts, ensuring you get the information you need quickly.
Sagot :
Sure, let's break down the solution step by step for Part D and Part E.
### Part D: Write the coordinates of two points on each line
Without the specific context or equations for Line A, Line B, and Line C, I will provide a generic framework. In general, to find two points on a line described by an equation [tex]\(y = mx + b\)[/tex] (where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept), you can select two values for [tex]\(x\)[/tex] and compute the corresponding [tex]\(y\)[/tex] values.
However, we need to imagine hypothetical data points for illustration purposes. Let's assume:
Line A:
Equation: [tex]\( y = 2x + 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) + 1 = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) + 1 = 5 \)[/tex]
Coordinates for Line A:
- Coordinate 1: [tex]\((0, 1)\)[/tex]
- Coordinate 2: [tex]\((2, 5)\)[/tex]
Line B:
Equation: [tex]\( y = 3x - 2 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = 3(0) - 2 = -2 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = 3(2) - 2 = 4 \)[/tex]
Coordinates for Line B:
- Coordinate 1: [tex]\((0, -2)\)[/tex]
- Coordinate 2: [tex]\((2, 4)\)[/tex]
Line C:
Equation: [tex]\( y = -x + 4 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = - (0) + 4 = 4 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = - (2) + 4 = 2 \)[/tex]
Coordinates for Line C:
- Coordinate 1: [tex]\((0, 4)\)[/tex]
- Coordinate 2: [tex]\((2, 2)\)[/tex]
#### Summary Table:
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline & Line A & Line B & Line C \\ \hline Coordinate 1 & (0, 1) & (0, -2) & (0, 4) \\ \hline Coordinate 2 & (2, 5) & (2, 4) & (2, 2) \\ \hline \end{tabular} \][/tex]
What information does each point represent for the sponsor's pledge plan?
Each point represents the relationship between two quantities. For instance:
- In Line A, point (0, 1) signifies that when there are 0 units (e.g., distance, events, items, etc.), the output is 1. The point (2, 5) indicates that for 2 units, the output is 5.
- Similar interpretations can be made for the other lines.
### Part E: Does each relationship represent a proportional relationship?
A proportional relationship between two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is described by [tex]\(y = kx\)[/tex] where [tex]\(k\)[/tex] is a constant. This implies that the graph of the relationship is a straight line passing through the origin (0, 0).
- Line A: [tex]\( y = 2x + 1 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of 1, not 0.
- Line B: [tex]\( y = 3x - 2 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of -2, not 0.
- Line C: [tex]\( y = -x + 4 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of 4, not 0.
In conclusion, none of the relationships for Line A, Line B, and Line C represent a proportional relationship as they do not pass through the origin.
### Part D: Write the coordinates of two points on each line
Without the specific context or equations for Line A, Line B, and Line C, I will provide a generic framework. In general, to find two points on a line described by an equation [tex]\(y = mx + b\)[/tex] (where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept), you can select two values for [tex]\(x\)[/tex] and compute the corresponding [tex]\(y\)[/tex] values.
However, we need to imagine hypothetical data points for illustration purposes. Let's assume:
Line A:
Equation: [tex]\( y = 2x + 1 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = 2(0) + 1 = 1 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = 2(2) + 1 = 5 \)[/tex]
Coordinates for Line A:
- Coordinate 1: [tex]\((0, 1)\)[/tex]
- Coordinate 2: [tex]\((2, 5)\)[/tex]
Line B:
Equation: [tex]\( y = 3x - 2 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = 3(0) - 2 = -2 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = 3(2) - 2 = 4 \)[/tex]
Coordinates for Line B:
- Coordinate 1: [tex]\((0, -2)\)[/tex]
- Coordinate 2: [tex]\((2, 4)\)[/tex]
Line C:
Equation: [tex]\( y = -x + 4 \)[/tex]
- When [tex]\( x = 0 \)[/tex]: [tex]\( y = - (0) + 4 = 4 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( y = - (2) + 4 = 2 \)[/tex]
Coordinates for Line C:
- Coordinate 1: [tex]\((0, 4)\)[/tex]
- Coordinate 2: [tex]\((2, 2)\)[/tex]
#### Summary Table:
[tex]\[ \begin{tabular}{|l|l|l|l|} \hline & Line A & Line B & Line C \\ \hline Coordinate 1 & (0, 1) & (0, -2) & (0, 4) \\ \hline Coordinate 2 & (2, 5) & (2, 4) & (2, 2) \\ \hline \end{tabular} \][/tex]
What information does each point represent for the sponsor's pledge plan?
Each point represents the relationship between two quantities. For instance:
- In Line A, point (0, 1) signifies that when there are 0 units (e.g., distance, events, items, etc.), the output is 1. The point (2, 5) indicates that for 2 units, the output is 5.
- Similar interpretations can be made for the other lines.
### Part E: Does each relationship represent a proportional relationship?
A proportional relationship between two variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is described by [tex]\(y = kx\)[/tex] where [tex]\(k\)[/tex] is a constant. This implies that the graph of the relationship is a straight line passing through the origin (0, 0).
- Line A: [tex]\( y = 2x + 1 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of 1, not 0.
- Line B: [tex]\( y = 3x - 2 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of -2, not 0.
- Line C: [tex]\( y = -x + 4 \)[/tex]
- This is not a proportional relationship because it has a y-intercept of 4, not 0.
In conclusion, none of the relationships for Line A, Line B, and Line C represent a proportional relationship as they do not pass through the origin.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.
