Answer: The graph is attached.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The line intersects the x-axis when [tex]y=0[/tex] .
Having the first equation:
[tex]y=−x+4[/tex]
Notice that:
[tex]b=4[/tex]
Substituting [tex]y=0[/tex] into the first equation and solving for "x", you get the x-intercept:
[tex]0=-x+4\\\\x=4[/tex]
Knowing that this line passes through the points [tex](0,4)[/tex] and [tex](4,0)[/tex], you can graph it.
Having the second equation:
[tex]18x+6y=−6[/tex]
We you must solve for "y":
[tex]18x+6y=-6\\\\6y=-18x-6\\\\y=-3x-1[/tex]
Notice that:
[tex]b=-1[/tex]
Substituting [tex]y=0[/tex] into threequation and solving for "x", you get that the x-intercept is:
[tex]0=-3x-1\\1=-3x\\\\x=-\frac{1}{3}[/tex]
Since the second line passes through the points [tex](0,-1)[/tex] and [tex](-\frac{1}{3},0)[/tex], we can graph it.
