Graph A displays a linear function.
To explain why, let's consider the characteristics of linear functions. A linear function can be represented by a straight line on a coordinate plane. It has the general form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Since Graph A goes through two specific points: (0, -3) and (2, 1), we can determine the slope between these points.
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To find the slope \( m \), we use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the points (0, -3) and (2, 1):
\[ m = \frac{1 - (-3)}{2 - 0} = \frac{1 + 3}{2} = \frac{4}{2} = 2 \]
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Now, we can write the equation of the line using the slope and one of the points (let's use (0, -3)):
\[ y = 2x - 3 \]
This equation is linear in form, confirming that the relationship between \( x \) and \( y \) is linear.
Additionally, since the graph passes through only two points and maintains a consistent slope, it will remain straight; thus supporting the conclusion that Graph A represents a linear function.
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