Answer:
The graph is shown below.
Step-by-step explanation:
Given:
[tex]y=-x+6\\8x-4y=-16[/tex]
In order to graph these two lines, we find their x and y intercepts.
The x intercept of [tex]y=-x+6[/tex] is at [tex]y=0[/tex]. So,
[tex]0=-x+6\\x=6[/tex]
Therefore, x intercept is at [tex](6,0)[/tex]
The y intercept of [tex]y=-x+6[/tex] is at [tex]x=0[/tex]. So,
[tex]y=0+6\\y=6[/tex]
Therefore, y intercept is at [tex](0,6)[/tex]
Now, similarly, we find the x and y intercepts of the other line.
The x intercept of [tex]8x-4y=-16[/tex] is at [tex]y=0[/tex]. So,
[tex]8x-4(0)=-16\\8x=-16\\x=\frac{-16}{8}=x=-2[/tex]
Therefore, x intercept is at [tex](-2,0)[/tex]
The y intercept of [tex]8x-4y=-16[/tex] is at [tex]x=0[/tex]. So,
[tex]8(0)-4y=-16\\-4y=-16\\y=frac{-16}{-4}=y=4[/tex]
Therefore, y intercept is at [tex](0,4)[/tex]
Now, we plot these pair of points on a graph and then join the pairs of lines.
The graph is shown below.
