To find the equation of a line in standard form that passes through the point \((-4, 2)\) with a slope of \(92\), we can start by using the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
Where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope. Substituting in our values:
\[ y - 2 = 92(x - (-4)) \]
This simplifies to:
\[ y - 2 = 92(x + 4) \]
Expanding the right side gives us:
\[ y - 2 = 92x + 368 \]
Adding 2 to both sides results in:
\[ y = 92x + 370 \]
Next, we will convert this equation into standard form \(Ax + By = C\). To do this, we can rearrange the equation:
\[ -92x + y = 370 \]
To put it in standard form, we often prefer \(Ax\) to be positive, so we can multiply the entire equation by \(-1\):
\[ 92x - y = -370 \]
Now let's put it in a more recognizable standard form \(Ax + By = C\):
\[ 92x - y = -370 \]
Now let's check which of the options provided corresponds to this equation. The options given in standard form are:
A. \(9x - 2y = 36\)
B. \(9x - 2y = 26\)
C. \(9x - 2y = -40\)
D. \(9x - 2y = -10\)
None of these options appear to have the correct coefficients when compared to the \(92x - 1y = -370\) format. It appears there may be a misunderstanding in the original slope or point, as all derived calculations lead to non-matching standard form equations.
Thus, we can conclude that none of the given options \(A\), \(B\), \(C\), or \(D\) are correct for the line with slope \(92\) passing through the point \((-4, 2)\).
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