To determine whether the line represented by the equation [tex]\( y = -6x + 1 \)[/tex] is increasing, decreasing, horizontal, or vertical, we need to examine the slope of the line.
The standard form of a linear equation is [tex]\( y = mx + b \)[/tex], where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, the point where the line crosses the y-axis.
In the equation [tex]\( y = -6x + 1 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-6\)[/tex].
A few points about the slope:
1. If the slope [tex]\( m \)[/tex] is positive, the line is increasing (it rises as you move from left to right).
2. If the slope [tex]\( m \)[/tex] is negative, the line is decreasing (it falls as you move from left to right).
3. If the slope [tex]\( m \)[/tex] is zero, the line is horizontal (it neither rises nor falls).
4. If the equation cannot be written in the form [tex]\( y = mx + b \)[/tex] or if [tex]\( x = \text{constant} \)[/tex], the line is vertical.
Here, since [tex]\( m = -6 \)[/tex], which is a negative number, we can conclude that the line is decreasing.
Therefore, the accurate description of the line [tex]\( y = -6x + 1 \)[/tex] is:
decreasing.
