To find an equation that represents the line that passes through the points (-1, 0) and (0, -2) in slope-intercept form (y = mx + b), we need to calculate the slope (m), then use one of the points to solve for b (the y-intercept).
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Calculate the slope (m) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (-1, 0) and (0, -2):
\[ m = \frac{-2 - 0}{0 - (-1)} = \frac{-2}{1} = -2 \]
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Use one of the points (we can use (0, -2) because it’s already at the y-intercept) to find b. The y-intercept (b) is the value of y when x = 0:
Hence, from the point (0, -2):
\[ b = -2 \]
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Write the equation in slope-intercept form using m and b:
\[ y = -2x - 2 \]
So the equation that represents the graph is
\[ \boxed{y = -2x - 2} \]
This matches the option given in your list.