The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 9 x 8
a = 72

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

8a² + 2a² = 10a²

The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 5) and (2, -5) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-5.0) - (5.0)}{(2) - (-2)} \) = \( \frac{-10}{4} \)
m = -2\(\frac{1}{2}\)

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -9) and (2, 1) so the slope becomes:

m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(1.0) - (-9.0)}{(2) - (-2)} \) = \( \frac{10}{4} \)
m = 2\(\frac{1}{2}\)

Plugging these values into the slope-intercept equation:

y = 2\(\frac{1}{2}\)x - 4

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)