To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

-4b + 6x = 8b + 9x + 1
-4b = 8b + 9x + 1 - 6x
-4b - 8b = 9x + 1 - 6x
-12b = 3x + 1
b = \( \frac{3x + 1}{-12} \)
b = \( \frac{3x}{-12} \) + \( \frac{1}{-12} \)
b = -\(\frac{1}{4}\)x - \(\frac{1}{12}\)

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

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, -2) and (2, 6) so the slope becomes:

Angles around a line add up to 180°. Angles around a point add up to 360°. When two lines intersect, adjacent angles are supplementary (they add up to 180°) and angles across from either other are vertical (they're equal).