To determine the inequality represented by the graph with points (-1, -2) to (0, 2), we first need to find the equation of the line that connects these two points.
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Calculate the slope (m) of the line: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-2)}{0 - (-1)} = \frac{4}{1} = 4 \]
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Use the point-slope form of the line's equation, using one of the points (let's use (0, 2)): \[ y - y_1 = m(x - x_1) \] Substituting the point (0, 2) and the slope 4: \[ y - 2 = 4(x - 0) \ y = 4x + 2 \]
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Determine the inequality. If the region above the line is shaded (which is often the case), the inequality would be: \[ y > 4x + 2 \] If the region below the line is shaded, then the inequality would be: \[ y < 4x + 2 \]
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Test for any solid or dashed line: If the line is dashed, that indicates that the inequality does not include the line itself (i.e., > or <). If the line is solid, it includes equality (i.e., ≥ or ≤).
With this information, you should be able to deduce the appropriate inequality based on the shading and the type of line (solid or dashed). If you need assistance with this part, please clarify how the graph appears (the shading and line type).