To derive the equation of the line in slope-intercept form \(y = mx + b\), we first need to find the slope \(m\) using the two given points \((1, -1)\) and \((0, -4)\).
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((1, -1)\) as \((x_1, y_1)\) and \((0, -4)\) as \((x_2, y_2)\):
\[ m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3 \]
So the slope \(m = 3\).
Next, we can use one of the points to find the y-intercept \(b\). We'll use the point \((0, -4)\):
In the slope-intercept form equation \(y = mx + b\):
Substituting \(m = 3\) and the point \((0, -4)\):
\[ -4 = 3(0) + b \]
This simplifies to:
\[ -4 = b \]
So the y-intercept \(b = -4\).
Now, we can put \(m\) and \(b\) together to write the equation of the line in slope-intercept form:
\[ y = 3x - 4 \]
This is the equation of the line that passes through the points \((1, -1)\) and \((0, -4)\).
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