To determine the slope of the line given by the equation [tex]\( y = -7x \)[/tex], let's follow the standard format for identifying the components of a linear equation.
The equation of a line in slope-intercept form is given as:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the y-intercept.
In the given equation:
[tex]\[ y = -7x \][/tex]
We can compare this to the general slope-intercept form:
[tex]\[ y = mx + b \][/tex]
In this comparison:
- The coefficient of [tex]\( x \)[/tex] here is [tex]\(-7\)[/tex], so this is the value of the slope [tex]\( m \)[/tex].
- Also, there is no constant term added or subtracted, which means the y-intercept [tex]\( b \)[/tex] is [tex]\( 0 \)[/tex], but the y-intercept is not necessary to identify for solving this particular question about the slope.
Hence, the slope of the line, which is represented by [tex]\( m \)[/tex], is:
[tex]\[ m = -7 \][/tex]
Therefore, the correct choice is:
C. -7
