To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

6y - 8 > \( \frac{y}{-4} \)
-4 x (6y - 8) > y
(-4 x 6y) + (-4 x -8) > y
-24y + 32 > y
-24y + 32 - y > 0
-24y - y > -32
-25y > -32
y > \( \frac{-32}{-25} \)
y > 1\(\frac{7}{25}\)

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

6b + x = -4
x = -4 - 6b

then substitute the result (-4 - 6b) into the second equation:

-2b + 4(-4 - 6b) = -1
-2b + (4 x -4) + (4 x -6b) = -1
-2b - 16 - 24b = -1
-2b - 24b = -1 + 16
-26b = 15
b = \( \frac{15}{-26} \)
b = -\(\frac{15}{26}\)

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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

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 = 1² + 1²
c² = 2
c = \( \sqrt{2} \)

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.

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, 3) so the slope becomes: