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

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The discussion centers on solving a linear function problem where z is defined as a linear function of x and y, with specified slopes of -1 in the x direction and 4 in the y direction. Participants seek to determine the change in z resulting from specific changes in x and y, as well as the value of z for given x and y coordinates. The correct approach involves understanding the relationship between the changes in x and y and their impact on z, using the formula Δz = -0.1 * (-1) + 0.3 * 4 for part a and applying the linear function definition for part b.

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  • Understanding of linear functions and their properties
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  • Basic algebraic manipulation skills
  • Knowledge of how to apply changes in variables to calculate effects on a function
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  • Study the concept of partial derivatives in multivariable calculus
  • Learn how to derive equations of linear functions from given slopes
  • Explore the application of linear approximations in real-world scenarios
  • Practice solving similar linear function problems with varying slopes
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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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