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} -(2y)/(-2)=-(Ax)/(-2)+(12)/(-2) \\ y=(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} (1)/(2)A=-3 \\ (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