To determine which graph is generated by the given table of values, we begin by translating the given pairs of [tex]\((x, y)\)[/tex] into a set of points.
The table provides the following pairs:
- When [tex]\(x = -4\)[/tex], [tex]\(y = 1\)[/tex]
- When [tex]\(x = 0\)[/tex], [tex]\(y = 2\)[/tex]
- When [tex]\(x = 3\)[/tex], [tex]\(y = 3\)[/tex]
From these pairs, we can generate the points:
1. [tex]\((-4, 1)\)[/tex]
2. [tex]\((0, 2)\)[/tex]
3. [tex]\((3, 3)\)[/tex]
Now, we plot these points on a coordinate plane.
1. Point (-4, 1):
- Starting from the origin (0,0), move 4 units to the left on the x-axis because [tex]\(x = -4\)[/tex].
- Then, move 1 unit up on the y-axis because [tex]\(y = 1\)[/tex].
- This location is [tex]\((-4, 1)\)[/tex].
2. Point (0, 2):
- Starting from the origin (0,0), [tex]\(x = 0\)[/tex] means no horizontal movement.
- Move 2 units up on the y-axis because [tex]\(y = 2\)[/tex].
- This location is [tex]\((0, 2)\)[/tex].
3. Point (3, 3):
- Starting from the origin (0,0), move 3 units to the right on the x-axis because [tex]\(x = 3\)[/tex].
- Then, move 3 units up on the y-axis because [tex]\(y = 3\)[/tex].
- This location is [tex]\((3, 3)\)[/tex].
By plotting these points on a graph, we obtain a visual representation of the relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. To graph these points:
1. Plot [tex]\((-4, 1)\)[/tex].
2. Plot [tex]\((0, 2)\)[/tex].
3. Plot [tex]\((3, 3)\)[/tex].
Connect these points with a straight line if you are examining a linear relationship or a curve if the relationship is non-linear. The specific type of graph will depend on the mathematical context, but these points accurately represent the data from the table.
