To find the equation of the line that passes through the given points \((2, 1)\), \((1, 5)\), and \((0, 9)\), we will first determine the slope (m) of the line using two of the points.
Let's use the points \((2, 1)\) and \((1, 5)\):
The slope \(m\) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values for \( (x_1, y_1) = (2, 1) \) and \( (x_2, y_2) = (1, 5) \): \[ m = \frac{5 - 1}{1 - 2} = \frac{4}{-1} = -4 \]
Now, using the slope-intercept form of the line \(y = mx + b\), where \(b\) is the y-intercept, we can substitute \(m = -4\) and one of the points to find \(b\). We'll use the point \((0, 9)\):
Substituting \(x = 0\) and \(y = 9\): \[ 9 = -4(0) + b \Rightarrow b = 9 \]
Thus, the equation of the line is: \[ y = -4x + 9 \]
Now, rearranging this into standard form \(Ax + By = C\): \[ 4x + y = 9 \]
From the equation \(4x + y = 9\), the values we need to fill in are:
- The coefficient of \(x\) is \(4\).
- The coefficient of \(y\) is \(1\).
- The constant term is \(9\).
Based on the options given, you can pick:
- 4 for the coefficient of \(x\),
- 1 for the coefficient of \(y\),
- 9 for the constant term.
Please let me know if you have any additional questions!
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