To graph the linear equation \( y = 2z - 3 \), it is important to note that this equation is in the form of \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Here, the y-intercept (\( b \)) is -3, which means the line crosses the y-axis at the point (0, -3). The slope (\( m \)) is 2, which indicates that for every unit increase in \( z \), \( y \) increases by 2 units.
To find another point, we can take a specific value for \( z \) and calculate \( y \).
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If \( z = 0 \): \[ y = 2(0) - 3 = -3 \quad \text{(Point is (0, -3))} \]
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If \( z = 1 \): \[ y = 2(1) - 3 = 2 - 3 = -1 \quad \text{(Point is (1, -1))} \]
Now we can plot these points: (0, -3) and (1, -1).
Let's compare these points to the options provided:
- Graph 1: (0, -1), (1, -3) - Does not match.
- Graph 2: (1, 5), (0, 3) - Does not match.
- Graph 3: (0, -3), (1, -1) - Matches. This is the correct graph for \( y = 2z - 3 \).
- Graph 4: (0, 1), (1, 4) - Does not match.
Thus, the correct graph for the equation \( y = 2z - 3 \) is Graph 3: (0, -3) and (1, -1).