Question

Suppose that z is a linear function of x and y with slope 3 in the x direction and slope 2 in the y direction.(a) A change of 0.2 in x and 0.1 in y produces what change in z? change in z=____________.(b) If z=5 when x=7 and y=4, what is the value of z when x=7.1 and y=3.8? z=________.

Answer 1

(a) 0.7

(b) 4.9

Explanation:

If z is a linear function of x and y and the slopes in the x and y directions are 3 and 2, respectively, z can be written as:

`z(x,y) = 3x+2y+c`

Where 'c' is a constant value.

(a) A change of 0.2 in x and 0.1 in y produces the following change in z:

`\Delta z = 2\Delta x +3\Delta y\\\Delta z = 2*0.2+3*0.1\\\Delta z = 0.7`

(b) Applying the point x=7, y=4, z=5 to the general equation gives us the value of 'c':

`5 = 3*7+2*4+c\\c= -24`

For x=7.1 and y=3.8, the value of z is:

`z(7.1, 3.8) = 3*7.1+2*3.8-24\\z= 4.9`