To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points \( p1(0, 1) \) and \( p2(1, -4) \), we can follow these steps:
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Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (0, 1) \) and \( (x_2, y_2) = (1, -4) \): \[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]
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Use the point-slope form of the line equation with one of the points to find the y-intercept (b). We can use point \( p1(0, 1) \): \[ y - y_1 = m(x - x_1) \] Plugging in \( m = -5 \), \( (x_1, y_1) = (0, 1) \): \[ y - 1 = -5(x - 0) \] \[ y - 1 = -5x \] \[ y = -5x + 1 \]
Now we have the equation of the line in slope-intercept form: \[ y = -5x + 1 \]
The correct option from your list is: y = −5x + 1.