To derive the equation of the line in slope-intercept form \(y = mx + b\) using the given coordinates \((0, -4)\) and \((1, -1)\), let's follow these steps:
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Identify the coordinates:
- Point 1: \((0, -4)\)
- Point 2: \((1, -1)\)
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Calculate the slope (m): The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates: \[ m = \frac{-1 - (-4)}{1 - 0} = \frac{-1 + 4}{1} = \frac{3}{1} = 3 \]
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Use the slope and one of the points to find the y-intercept (b): We can use the y-intercept from point (0, -4) directly: Since the line passes through (0, -4), the y-intercept \(b\) is \(-4\).
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Write the equation in slope-intercept form: Now that we have \(m = 3\) and \(b = -4\), we can substitute these values into the slope-intercept formula: \[ y = 3x - 4 \]
Thus, the equation of the line in slope-intercept form is: \[ \boxed{y = 3x - 4} \]