To find the missing coefficient, first, write the equation in slope-intercept form:
[tex]Ax-2y=12[/tex]
-Subtract Ax
[tex]\begin{gathered} Ax-Ax-2y=12-Ax \\ -2y=-Ax+12 \end{gathered}[/tex]
-Divide both sides by -2
[tex]\begin{gathered} -\frac{2y}{-2}=-\frac{Ax}{-2}+\frac{12}{-2} \\ y=\frac{1}{2}Ax-6 \end{gathered}[/tex]
The slope of the line is expressed by the coefficient 1/2A, this value should be "-3", then:
[tex]\begin{gathered} \frac{1}{2}A=-3 \\ \frac{1}{2}A\cdot2=(-3)\cdot2 \\ A=-6 \end{gathered}[/tex]
For the slope of the line to be m=-3, the coefficient must be A=-3
