To derive the equation of the line in slope-intercept form (i.e., \( y = mx + b \)), we need to determine the slope (\( m \)) and the y-intercept (\( b \)).
The given points are \((1, -1)\) and \((0, -4)\).
### Step 1: Determine the slope (\( m \))
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substitute the given points \((1, -1)\) and \((0, -4)\) into the formula:
\[ m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3 \]
So, the slope \( m \) is \( 3 \).
### Step 2: Determine the y-intercept (\( b \))
The y-intercept can be found by using one of the points and the slope in the slope-intercept equation \( y = mx + b \).
Let's use the point \((0, -4)\), which is the y-intercept:
\[ -4 = 3(0) + b \]
\[ -4 = b \]
So, the y-intercept \( b \) is \(-4\).
### Step 3: Write the equation of the line
Substitute \( m = 3 \) and \( b = -4 \) into the slope-intercept form \( y = mx + b \):
\[ y = 3x - 4 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = 3x - 4 \]
(1,-1) and (0,-4) derive the equation of the line in slope intercept form
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