To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) using the two points provided: (0, 2) and (1, -1).
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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:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (0, 2)\) and \((x_2, y_2) = (1, -1)\).
\[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
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Use one point to find the y-intercept (b): We can use the point (0, 2), the y-intercept is simply \( b = 2 \).
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Write the equation: Now that we have \( m \) and \( b \), we can write the equation of the line:
\[ y = -3x + 2 \]
Thus, the equation of the line in slope-intercept form is \( y = -3x + 2 \).
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