To determine the slope of the line represented by the equation [tex]\( y = x - 9 \)[/tex], we start by examining the general form of a linear equation. The standard form of a line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] is the y-intercept.
In the given equation:
[tex]\[ y = x - 9 \][/tex]
we can see that it matches the form [tex]\( y = mx + b \)[/tex]. Here, [tex]\( x \)[/tex] is the variable term, and it has a coefficient, while [tex]\(-9\)[/tex] represents the y-intercept.
To find the slope, we identify the coefficient of [tex]\( x \)[/tex] in the equation. The equation can be rewritten as:
[tex]\[ y = 1x - 9 \][/tex]
From this, we observe that the coefficient of [tex]\( x \)[/tex] (which is [tex]\( m \)[/tex]) is [tex]\( 1 \)[/tex]. Therefore, the slope of the line is:
[tex]\[ \boxed{1} \][/tex]
