To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points provided: (1, -1) and (0, -4).
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Calculate the slope (m): The formula for the slope between two points (x1, y1) and (x2, y2) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's substitute the points into this formula:
- Point 1 (x1, y1) = (1, -1)
- Point 2 (x2, y2) = (0, -4)
\[ m = \frac{-4 - (-1)}{0 - 1} = \frac{-4 + 1}{-1} = \frac{-3}{-1} = 3 \]
So, the slope \( m = 3 \).
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Use the slope to find the y-intercept (b): The y-intercept (b) can be directly obtained from the point (0, -4), which corresponds to the y-coordinate when x = 0. Thus, \( b = -4 \).
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Write the equation in slope-intercept form: Now that we have both the slope (m) and the y-intercept (b), we can write the equation of the line:
\[ y = 3x - 4 \]
Therefore, the equation of the line in slope-intercept form is:
\[ y = 3x - 4 \]