Question

Find the value of the missing coefficient in the equation Ax-2y=12 so that the line will have the slope -3

Answer 1

To find the missing coefficient, first, write the equation in slope-intercept form:

$Ax-2y=12$

-Subtract Ax

$\begin{gathered} Ax-Ax-2y=12-Ax \\ -2y=-Ax+12 \end{gathered}$

-Divide both sides by -2

$\begin{gathered} -\frac{2y}{-2}=-\frac{Ax}{-2}+\frac{12}{-2} \\ y=\frac{1}{2}Ax-6 \end{gathered}$

The slope of the line is expressed by the coefficient 1/2A, this value should be "-3", then:

$\begin{gathered} \frac{1}{2}A=-3 \\ \frac{1}{2}A\cdot2=(-3)\cdot2 \\ A=-6 \end{gathered}$

For the slope of the line to be m=-3, the coefficient must be A=-3