To determine the equation of the line in standard form, we'll first identify the key points you provided: (-3, 5) and (-1, -3). Next, we can follow these steps:
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Find the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] With points (-3, 5) and (-1, -3): \[ m = \frac{-3 - 5}{-1 - (-3)} = \frac{-8}{-1 + 3} = \frac{-8}{2} = -4 \]
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Use point-slope form: The point-slope form of the linear equation is: \[ y - y_1 = m(x - x_1) \] Using one of the points, (-3, 5): \[ y - 5 = -4(x + 3) \]
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Convert to standard form: First, simplify the equation: \[ y - 5 = -4x - 12 \] Bringing y to the left: \[ y = -4x - 7 \] Now, move everything to one side to get it into standard form (Ax + By = C): \[ 4x + y = -7 \]
So the equation of the line in standard form is:
4x + y = -7.
Among the responses you provided, that matches the first option.