To determine the slope and y-intercept of the line passing through the points \((-4, 3)\), \((0, 1)\), and \((2, 0)\), we can use the coordinates provided.
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Calculating the Slope (m): The slope \(m\) can be calculated using any two points on the line with the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points \((0, 1)\) and \((2, 0)\): \[ m = \frac{0 - 1}{2 - 0} = \frac{-1}{2} = -\frac{1}{2} \]
We can also check the slope using the points \((-4, 3)\) and \((0, 1)\): \[ m = \frac{1 - 3}{0 - (-4)} = \frac{-2}{4} = -\frac{1}{2} \]
The slope should remain consistent across any two points that lie on the line, confirming our slope.
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Finding the y-intercept (b): The y-intercept can be determined directly from the point where \(x = 0\). From the point \((0, 1)\), we see that the y-intercept \(b\) is 1.
Now we can summarize the results:
- Slope: \( -\frac{1}{2} \)
- Y-intercept: \( 1 \)
From the given options, none seem to have a matching slope of \(-\frac{1}{2}\). The calculations show that there's a potential mismatch in options provided.
If we take previously evaluated options:
- \(slope: -2; y-intercept: 2 (Not matching)\)
- \(slope: ; y-intercept: 1 (Not complete)\)
- \(slope: ; y-intercept: 2 (Not complete)\)
- \(slope: 2; y-intercept: 1 (Not matching)\)
It appears none of those matches adequately reflect the calculated slope of \(-\frac{1}{2}\) and y-intercept of \(1\). If there is any opportunity to revisit the data or points to confirm the slope calculation, it could clarify the mismatch in expected answers.