To find the equation of the line in the form \( y = mx + b \), we can use the two points given: \( (1, 0) \) and \( (0, -3) \).
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Calculate the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \( (1, 0) \) and \( (0, -3) \):
- \( (x_1, y_1) = (1, 0) \)
- \( (x_2, y_2) = (0, -3) \)
Plugging in the values: \[ m = \frac{-3 - 0}{0 - 1} = \frac{-3}{-1} = 3 \]
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Find the y-intercept (b): The y-intercept \( b \) can be found from one of the points. Since the second point is \( (0, -3) \), it directly gives us the y-intercept: \[ b = -3 \]
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Write the equation: Now, substituting \( m \) and \( b \) into the line equation \( y = mx + b \): \[ y = 3x - 3 \]
Therefore, the correct equation of the line is: C. \( y = 3x - 3 \).