To find the equation of the line that passes through the points (2, 1), (1, 5), and (0, 9), we can start by calculating the slope \( m \) of the line using two of the given points. Let's use the points (2, 1) and (0, 9):
The formula for slope \( m \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (2, 1) as \( (x_1, y_1) \) and (0, 9) as \( (x_2, y_2) \):
\[ m = \frac{9 - 1}{0 - 2} = \frac{8}{-2} = -4 \]
Now that we have the slope \( m = -4 \), we can use the point-slope form of the equation of the line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Using the point (2, 1):
\[ y - 1 = -4(x - 2) \]
Expanding this equation:
\[ y - 1 = -4x + 8 \] \[ y = -4x + 9 \]
So, the equation of the line is:
\[ y = -4x + 9 \]
You can also represent this in the standard form \( Ax + By = C \) if needed:
Rearranging gives:
\[ 4x + y = 9 \]
Thus, you can drag numbers to represent either:
- Slope: \(-4\)
- Intercept: \(9\) (for \(y\)-intercept)
- Rearranged standard form: \(4\), \(1\), \(9\) (for \(4x + y = 9\))
Feel free to clarify if you need specific help regarding the dragging or if there are boxes with values needed.
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