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 given points (0, 2) and (1, -1).
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Calculate the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Plugging in the points \((0, 2)\) and \((1, -1)\):
\[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]
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Use the slope to find the y-intercept (b): We can use one of the points along with the slope to solve for b. We'll use the point \((0, 2)\):
The slope-intercept form is:
\[ y = mx + b \]
Substituting the values we have:
\[ 2 = -3(0) + b \]
\[ 2 = b \]
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Write the equation of the line: Now that we have both 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:
\[ y = -3x + 2 \]