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Question 7 of 11

A jogger is running home. His distance from home, as a function of time, is modeled by [tex]y = -7x + 8[/tex].

Which statement best describes the function?

A. The function is linear at some points and nonlinear at other points.
B. The function is linear.
C. The function is nonlinear.
D. Not enough information is given to decide.

Sagot :

GinnyAnswer
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.
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