Let's analyze the function given:
The function describing the jogger's distance from home as a function of time is [tex]\( y = -7x + 8 \)[/tex].
To understand this function, we need to identify its form:
1. Recognize the format: [tex]\( y = -7x + 8 \)[/tex] is in the standard linear form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. The slope [tex]\( m \)[/tex] in this equation is [tex]\(-7\)[/tex]. A linear function always has a constant slope, which means the rate of change is consistent regardless of the value of [tex]\( x \)[/tex].
3. The y-intercept [tex]\( b \)[/tex] is [tex]\( 8 \)[/tex], which indicates the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
Given this information, let's evaluate each option:
A) The function is linear at some points and nonlinear at other points.
- This option suggests that the function's form changes between linear and nonlinear, which is not true for [tex]\( y = -7x + 8 \)[/tex].
B) The function is linear.
- This statement aligns perfectly with the form of the given function. Since [tex]\( y = -7x + 8 \)[/tex] consistently follows a linear relationship throughout, this is the correct description.
C) The function is nonlinear.
- This statement is incorrect because [tex]\( y = -7x + 8 \)[/tex] fits the definition of a linear function.
D) Not enough information is given to decide.
- This option is incorrect because the form of the function [tex]\( y = -7x + 8 \)[/tex] provides all the necessary information to determine that it is linear.
Therefore, the statement that best describes the function is:
B. The function is linear.
