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

[KTiaam]

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.

 

[Mark44]

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.

Any help to start this problem with help me thank you.

 

[KTiaam]

Δz = Δx +Δy

 

[Mark44]

What does the phrase "z is a linear function of x and y" mean to you? That's an important part of this problem.

Δz = Δx +Δy

That's not what it means.