To write the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).
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Calculate the slope (m): The formula for 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 (0, -2) and (4, -1):
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (4, -1) \)
So the slope is:
\[ m = \frac{-1 - (-2)}{4 - 0} = \frac{-1 + 2}{4} = \frac{1}{4} \]
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Identify the y-intercept (b): The y-intercept is the point where the line crosses the y-axis. From the given point (0, -2), we can see that:
\[ b = -2 \]
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Write the equation in slope-intercept form: Now that we have the slope (m = \(\frac{1}{4}\)) and the y-intercept (b = -2), we can write the equation:
\[ y = \frac{1}{4}x - 2 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{1}{4}x - 2 \]
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