Question 1190621
Here's the breakdown of this rectangle problem:

**a) Units:**

*   Row 1 (Width): meters (m)
*   Row 2 (Area): square meters (m²)
*   Row 3 (Perimeter): meters (m)

**b) Linear Function?**

Perimeter *could* be a linear function of side length (width).  As the width increases by 1 meter, the perimeter increases by a consistent 6 meters.  Area, however, is *not* linear.  The increase in area is not constant as the width increases.

**c) Perimeter as a function of x (width):**

Since the length is twice the width, let:

*   x = width
*   2x = length

Perimeter = 2(length + width)
Perimeter = 2(2x + x)
Perimeter = 2(3x)
P(x) = 6x

**d) Area as a function of x (width):**

Area = length * width
Area = (2x) * x
A(x) = 2x²

**e) Linear Relationship:**

The perimeter is a linear function of the width.  The rate of change (slope) is 6.  This means that for every 1-meter increase in the width of the rectangle, the perimeter increases by 6 meters.

**f) Graphs:**

I can't physically draw graphs here, but I'll describe how they should look:

*   **Area vs. Width:** The graph of area vs. width should be a curve (specifically, a parabola opening upwards). The points you would plot are (0,0), (1,2), (2,8), (3,18), (4,32), (5,50), and (6,72).

*   **Perimeter vs. Width:** The graph of perimeter vs. width should be a straight line. The points you would plot are (0,0), (1,6), (2,12), (3,18), (4,24), (5,30), and (6,36).