Question

use the situation to answer the questions.
a function is used to calculate the side length of a square based upon the area of the square. the side length is calculated by the following formula:
$s = \sqrt{a}$, where $s$ is the side length and $a$ is the area
the formula could also be written using $x$ and $y$:
$y = \sqrt{x}$, where $y$ is the side length and $x$ is the area

1. assuming the area is measured in square meters, complete the table of values.

area ($\text{m}^2$) $x$	process $\sqrt{x}$	side length (m) $y$
1
2.25
4

1. plot the points and see if they form a straight line.

(graph with x - axis: area of square ($\text{m}^2$), y - axis: side length (m))

Explanation:

Step1: Calculate for \( x = 0.25 \)

We use the formula \( y=\sqrt{x} \). Substitute \( x = 0.25 \) into the formula: \( \sqrt{0.25} \). Since \( 0.5\times0.5 = 0.25 \), \( \sqrt{0.25}=0.5 \). So the process is \( \sqrt{0.25} \) and the side length \( y = 0.5 \).

Step2: Calculate for \( x = 1 \)

Using the formula \( y=\sqrt{x} \), substitute \( x = 1 \): \( \sqrt{1} \). Since \( 1\times1 = 1 \), \( \sqrt{1}=1 \). The process is \( \sqrt{1} \) and the side length \( y = 1 \).

Step3: Calculate for \( x = 2.25 \)

Substitute \( x = 2.25 \) into \( y=\sqrt{x} \): \( \sqrt{2.25} \). Since \( 1.5\times1.5 = 2.25 \), \( \sqrt{2.25}=1.5 \). The process is \( \sqrt{2.25} \) and the side length \( y = 1.5 \).

Step4: Calculate for \( x = 4 \)

Substitute \( x = 4 \) into \( y=\sqrt{x} \): \( \sqrt{4} \). Since \( 2\times2 = 4 \), \( \sqrt{4}=2 \). The process is \( \sqrt{4} \) and the side length \( y = 2 \).

For the table:

Area (\( m^2 \)) \( x \)	Process \( \sqrt{x} \)	Side Length (m) \( y \)
1	\( \sqrt{1} \)	1
2.25	\( \sqrt{2.25} \)	1.5
4	\( \sqrt{4} \)	2

For part 2, when we plot the points \((0.25, 0.5)\), \((1, 1)\), \((2.25, 1.5)\), \((4, 2)\), we can see that the slope between \((0.25, 0.5)\) and \((1, 1)\) is \( \frac{1 - 0.5}{1 - 0.25}=\frac{0.5}{0.75}=\frac{2}{3}\), between \((1, 1)\) and \((2.25, 1.5)\) is \( \frac{1.5 - 1}{2.25 - 1}=\frac{0.5}{1.25}=\frac{2}{5}\), which are not equal. So the points do not form a straight line (they form a curve, as \( y = \sqrt{x} \) is a square - root function, a non - linear function).

Answer:

1. The completed table is as above. 2) The points do not form a straight line.