To derive the equation of the line in slope-intercept form \(y = mx + b\) using the points (1, -1) and (0, -4), we follow these steps:
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Identify the points:
- Point 1: \((x_1, y_1) = (1, -1)\)
- Point 2: \((x_2, y_2) = (0, -4)\)
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Calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values from the points: \[ m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3 \]
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Use the slope and one of the points to find the y-intercept \(b\). We'll use the point (0, -4) since it already provides the y-intercept directly: \[ b = -4 \]
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Write the equation in slope-intercept form: Substitute \(m\) and \(b\) into the equation \(y = mx + b\): \[ y = 3x - 4 \]
Thus, the equation of the line in slope-intercept form is: \[ y = 3x - 4 \]