To find the slope of a line parallel to the line given by the equation [tex]\( x + y = -7 \)[/tex], we first need to determine the slope of the original line. This can be done by rewriting the equation in slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope.
Starting with the given equation:
[tex]\[ x + y = -7 \][/tex]
We need to isolate [tex]\( y \)[/tex]. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ y = -x - 7 \][/tex]
The equation is now in the form [tex]\( y = mx + b \)[/tex]. Here, the coefficient of [tex]\( x \)[/tex] (which is [tex]\(-1\)[/tex]) represents the slope [tex]\( m \)[/tex].
Thus, the slope of the given line is:
[tex]\[ m = -1 \][/tex]
Lines that are parallel have the same slope. Therefore, a line parallel to the line [tex]\( x + y = -7 \)[/tex] will also have a slope of:
[tex]\[ -1 \][/tex]
So, the slope of the line parallel to the line [tex]\( x + y = -7 \)[/tex] is:
[tex]\[ -1 \][/tex]
