The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(6 + 4)(3)
a = ½(10)(3)
a = ½(30) = \( \frac{30}{2} \)
a = 15

You need to find the value of c so solve the first equation in terms of x:

c + x = -2
x = -2 - c

then substitute the result (-2 - 1c) into the second equation:

-2c - 7(-2 - c) = -4
-2c + (-7 x -2) + (-7 x -c) = -4
-2c + 14 + 7c = -4
-2c + 7c = -4 - 14
5c = -18
c = \( \frac{-18}{5} \)
c = -3\(\frac{3}{5}\)

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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 -3. 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, -4) and (2, -2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = \(\frac{1}{2}\)x - 3