EXPLANATION :
From the problem, we have the equation :
[tex]x+4y=-6[/tex]
Rewrite the equation into slope intercept form y = mx + b
[tex]\begin{gathered} x+4y=-6 \\ 4y=-x-6 \\ y=-\frac{1}{4}x-\frac{3}{2} \end{gathered}[/tex]
We need two points to graph the equation :
Let x = -2 :
[tex]y=-\frac{1}{4}(-2)-\frac{3}{2}=-1[/tex]
Let x = 2 :
[tex]y=-\frac{1}{4}(2)-\frac{3}{2}=-2[/tex]
So the points are (-2, -1) and (2, -2)
Plot the points :
