Answer:
We conclude the equation is linear because it can be rewritten in the form [tex]y = mx + b[/tex].
Hence, option D is correct.
Step-by-step explanation:
The slope-intercept form of the line or linear equation
[tex]y = mx+b[/tex]
where
Important Tip:
The graph of a linear equation is always a straight line.
Convert the given equation in the slope-intercept form
[tex]18x + 9y = -416[/tex]
subtract 18x from both sides
[tex]18x+9y-18x = - 18x-416[/tex]
simplify
[tex]9y = -18x - 416[/tex]
divide both sides by 9
[tex]y=-2x-\frac{416}{9}[/tex]
Now, comparing the equation [tex]y=-2x-\frac{416}{9}[/tex] with a slop-intercept form of linear equation
Therefore, we conclude the equation is linear because it can be rewritten in the form [tex]y = mx + b[/tex].
From the attached graph, is also clear that the graph of the equation [tex]y=-2x-\frac{416}{9}[/tex] is a straight line.
Hence, option D is correct.
