We are given the equation:
[tex]3y=-\frac{6}{4}(x+4)+12[/tex]
We need to solve the equation for the x-intercept. We first need to simplify the given equation into slope-intercept form.
[tex]\begin{gathered} \frac{3y}{3}=\frac{-\frac{6}{4}(x+4)+12}{3} \\ \\ y=-\frac{1}{2}x-2+4_{} \\ y=-\frac{x-4}{2} \end{gathered}[/tex]
Then, we will set y = 0 and solve for x to find the x-intercept.
[tex]\begin{gathered} 0=-\frac{x-4}{2} \\ 0=-x-4 \\ 4=-x \\ -x=4 \\ x=-4 \end{gathered}[/tex]
Therefore, the x-intercept is located where y = 0. This means that our coordinate pair will be (-4, 0).
