To identify the constant term [tex]\(b\)[/tex] and the coefficient [tex]\(m\)[/tex] in the expression [tex]\(b + mx\)[/tex] for the linear function [tex]\(f(x) = 200 - 16x\)[/tex], we will compare this function to the standard form of a linear equation, which is written as [tex]\( f(x) = b + mx \)[/tex].
1. Identify the constant term [tex]\(b\)[/tex]:
- In the standard form [tex]\( f(x) = b + mx \)[/tex], [tex]\(b\)[/tex] represents the constant term, which is the term without the variable [tex]\(x\)[/tex].
- By examining the given function [tex]\( f(x) = 200 - 16x \)[/tex], we see that the term without [tex]\(x\)[/tex] is [tex]\( 200 \)[/tex].
- Therefore, the constant term [tex]\( b \)[/tex] is [tex]\( 200 \)[/tex].
2. Identify the coefficient [tex]\(m\)[/tex]:
- In the standard form [tex]\( f(x) = b + mx \)[/tex], [tex]\(m\)[/tex] is the coefficient of the variable [tex]\(x\)[/tex].
- By examining the given function [tex]\( f(x) = 200 - 16x \)[/tex], we see that the coefficient of [tex]\(x\)[/tex] is [tex]\( -16 \)[/tex].
- Therefore, the coefficient [tex]\( m \)[/tex] is [tex]\( -16 \)[/tex].
So, the identified values are:
[tex]\[
\begin{array}{c}
b = 200 \\
m = -16
\end{array}
\][/tex]
Final answers:
[tex]\[
\boxed{b = 200}
\][/tex]
[tex]\[
\boxed{m = -16}
\][/tex]
