Question

Which of these describes the equation –18x + 9y = –416?

A
The equation is not linear because it has 2 variables, not 1.
B
The equation is not linear because it is not in the form y = mx + b.
С
The equation is linear because it has variables with exponents of 0.
D
The equation is linear because it can be rewritten in the form y = mx + b.

Answer 1

Answer:D

Explanation:

Answer 2

We conclude the equation is linear because it can be rewritten in the form
`y = mx + b`.

Hence, option D is correct.

Explanation:

The slope-intercept form of the line or linear equation

`y = mx+b`

where

• 
  `m` is the slope

• 
  `b` is the y-intercept

Important Tip:

The graph of a linear equation is always a straight line.

Convert the given equation in the slope-intercept form

`18x + 9y = -416`

subtract 18x from both sides

`18x+9y-18x = - 18x-416`

simplify

`9y = -18x - 416`

divide both sides by 9

`y=-2x-(416)/(9)`

Now, comparing the equation
`y=-2x-(416)/(9)` with a slop-intercept form of linear equation

• The slope m = -2

• The y-intercept b = -416/9

Therefore, we conclude the equation is linear because it can be rewritten in the form
`y = mx + b`.

From the attached graph, is also clear that the graph of the equation
`y=-2x-(416)/(9)` is a straight line.

Hence, option D is correct.