To determine which point is not a solution to the function represented by the line passing through the points (0, -5) and (2.5, 0), we need to find the equation of the line.
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Find the slope (m) of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using the points (0, -5) and (2.5, 0):
\[ m = \frac{0 - (-5)}{2.5 - 0} = \frac{5}{2.5} = 2 \]
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Use the point-slope form (y - y_1 = m(x - x_1)) to find the equation of the line. Using the point (0, -5):
\[ y - (-5) = 2(x - 0) \Rightarrow y + 5 = 2x \Rightarrow y = 2x - 5 \]
Now, we can use this equation \( y = 2x - 5 \) to evaluate whether specific points are solutions to the function.
You can check different points to see if they satisfy this equation. For example:
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For the point (0, -5): \[ y = 2(0) - 5 = -5 \quad \text{(solution)} \]
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For the point (2.5, 0): \[ y = 2(2.5) - 5 = 5 - 5 = 0 \quad \text{(solution)} \]
If you provide any potential point you want to check, I can help determine if it is or is not a solution.
For example, if we check the point (1, -3): \[ y = 2(1) - 5 = 2 - 5 = -3 \quad \text{(solution)} \]
But if we check the point (1, -2): \[ y = 2(1) - 5 = 2 - 5 = -3 \quad \text{(-2 is not a solution)} \]
Please provide specific points you would like to check, and I'll determine which is not a solution!