We are given the following equation:
[tex]x+4y=-6[/tex]We can solve for "y" first by subtracting x to both sides:
[tex]4y=-6-x[/tex]now we divide both sides by 4:
[tex]y=-\frac{6}{4}-\frac{x}{4}[/tex]Simplifying:
[tex]y=-\frac{3}{2}-\frac{x}{4}[/tex]Since the equation is of the form:
[tex]y=mx+b[/tex]This is the equation of a line. Therefore, to plot this line we only need to points. We find the points by giving values to "x".
For x = 0:
[tex]\begin{gathered} y=-\frac{3}{2}-(0)\frac{1}{4} \\ y=-\frac{3}{2} \end{gathered}[/tex]Therefore the point (0, -3/2) is part of the line.
For x = 1
[tex]\begin{gathered} y=-\frac{3}{2}-\frac{1}{4} \\ y=-\frac{7}{4} \end{gathered}[/tex]therefore, the point (1, -7/4) is part of the line. Now we plot this to points and join them with a line, like this:
