Solving Linear Function Homework: z=? for x,y Change & z=? for x,y Values

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Homework Help Overview

The problem involves understanding a linear function z in relation to variables x and y, specifically focusing on how changes in x and y affect z. The context includes determining the change in z due to specified changes in x and y, as well as finding the value of z for given x and y values.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to begin solving the problem and question the meaning of the slopes provided. There is mention of potentially setting up a system of equations to find z.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the meaning of the slopes in the context of a linear function. Some have attempted to express relationships between changes in variables, but there is no consensus on the approach to take.

Contextual Notes

Participants are grappling with the definitions and implications of the slopes in the linear function, as well as the overall meaning of z being a linear function of x and y. There is a lack of explicit information on how to relate these concepts to the changes in z.

KTiaam
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Homework Statement


Suppose that z is a linear function of x and y with slope -1 in the x direction and slope 4 in the y direction.

Part a)
A change of −0.1 in x and 0.3 in y produces what change in z?
z = ?

Part b)
If z=5 when x=7 and y=6, what is the value of z when x=7.1 and y=5.7?
z = ?

Homework Equations

The Attempt at a Solution



I really do not know where to start with this problem.
Maybe setting a system of equations and solving for z?
What does the "with slope -1 in the x direction and slope of 4 in the y direction" mean?Any help to start this problem with help me thank you.
 
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KTiaam said:

Homework Statement


Suppose that z is a linear function of x and y with slope -1 in the x direction and slope 4 in the y direction.

Part a)
A change of −0.1 in x and 0.3 in y produces what change in z?
z = ?

Part b)
If z=5 when x=7 and y=6, what is the value of z when x=7.1 and y=5.7?
z = ?

Homework Equations

The Attempt at a Solution



I really do not know where to start with this problem.
Maybe setting a system of equations and solving for z?

What does the "with slope -1 in the x direction and slope of 4 in the y direction" mean?
What does the phrase "z is a linear function of x and y" mean to you? That's an important part of this problem.
KTiaam said:
Any help to start this problem with help me thank you.
 
Δz = Δx +Δy
 
Mark44 said:
What does the phrase "z is a linear function of x and y" mean to you? That's an important part of this problem.
KTiaam said:
Δz = Δx +Δy
That's not what it means.
 

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