Question

A line is drawn through (–4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?

The line represents a direct variation because = .
The line represents a direct variation because it is horizontal.
The line does not represent a direct variation because it does not go through the origin.
The line does not represent a direct variation because –4(3) ≠ 4(3).

Answer 1

A line y= k x, represents a direct variation if ,
`k=(y)/(x)`

As,line passes through (-4,3) and (4,3).

Equation of line passing through two points is,

`(y-3)/(x+4)=(3-3)/(4+4)\\\\ y-3=0`

Given by the formula:
`(y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))`

As, the line does not pass through origin , so the line passing through (-4,3) and (4,3) does not represent direct variation.

Option (C)=The line does not represent a direct variation because it does not go through the origin.

Answer 2

The line does not represent direct variation because it does not go through the origin. In fact, it happens to be a horizontal line whose equation is : y = 3.