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Find an equation of the line with the given slope that passes through the given point. Write the equation in the form $A x+B y=C$. $m=-4,(-5,-6)$
The equation of the line in the form $A x+B y=C$ is $\square$.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Final Answer: The equation of the line in the form \(A x+B y=C\) is \(\boxed{4x + y = -26}\).
Step 1 :Given the slope of the line, m = -4, and a point on the line (-5,-6).
Step 2 :We can use the point-slope form of the line equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the given point.
Step 3 :Substitute the given values into the equation, we get \(y - (-6) = -4(x - (-5))\).
Step 4 :Simplify the equation to get \(y + 6 = -4x - 20\).
Step 5 :Rearrange this equation to the form \(Ax + By = C\), we get \(4x + y = -26\).
Step 6 :Final Answer: The equation of the line in the form \(A x+B y=C\) is \(\boxed{4x + y = -26}\).