To find the linear function with the given properties, we need to use the information provided:
1. The function value at [tex]\( x = 0 \)[/tex], given by [tex]\( f(0) = -7 \)[/tex], indicates the [tex]\( y \)[/tex]-intercept of the linear function.
2. The slope ([tex]\( m \)[/tex]) of the function is given as [tex]\( -1 \)[/tex].
A linear function can be written in the form:
[tex]\[ f(x) = mx + c \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept.
Given:
- The slope [tex]\( m = -1 \)[/tex]
- The [tex]\( y \)[/tex]-intercept [tex]\( c = -7 \)[/tex]
We substitute these values into the linear function form:
[tex]\[ f(x) = -1x + (-7) \][/tex]
Thus, the linear function is:
[tex]\[ f(x) = -1x - 7 \][/tex]
So, the linear function with the given properties is:
[tex]\[ f(x) = -x - 7 \][/tex]
Therefore, the slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex], the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is [tex]\(-7\)[/tex], and the equation of the linear function is:
[tex]\[ f(x) = -x - 7 \][/tex]
