Question

match the graph to the correct description
x y
-2 -7
-1 -4
0 -1
1 2
2 5

responses
nonlinear; function
nonlinear; not a function
linear; function
linear; not a function

Answer 1

To determine the correct description for the given set of coordinates, we first need to analyze the points and check two main criteria: whether the relationship is linear and whether it is a function.

1. **Check if it's a function**: A relation is a function if each input (x-value) corresponds to exactly one output (y-value). The given points are:
- (-2, -7)
- (-1, -4)
- (0, -1)
- (1, 2)
- (2, 5)

All x-values are unique; therefore, this is a function.

2. **Check if it's linear**: A linear relationship produces points that can be connected to form a straight line. To determine if the relationship is linear, we calculate the slopes between the points:

- Slope between (-2, -7) and (-1, -4):
\[\text{slope} = \frac{-4 - (-7)}{-1 - (-2)} = \frac{3}{1} = 3\]
- Slope between (-1, -4) and (0, -1):
\[\text{slope} = \frac{-1 - (-4)}{0 - (-1)} = \frac{3}{1} = 3\]
- Slope between (0, -1) and (1, 2):
\[\text{slope} = \frac{2 - (-1)}{1 - (0)} = \frac{3}{1} = 3\]
- Slope between (1, 2) and (2, 5):
\[\text{slope} = \frac{5 - 2}{2 - 1} = \frac{3}{1} = 3\]

Since the slope is consistent between all points, the relationship is linear.

Based on the analysis, the correct description for the given graph is:
**linear; function**.