A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

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.

3b + 6z = 5b - 5z - 2
3b = 5b - 5z - 2 - 6z
3b - 5b = -5z - 2 - 6z
-2b = -11z - 2
b = \( \frac{-11z - 2}{-2} \)
b = \( \frac{-11z}{-2} \) + \( \frac{-2}{-2} \)
b = 5\(\frac{1}{2}\)z + 1

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

a = l x w
a = a x b
a = 3 x 4
a = 12

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

AD = AB + BD

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 2 as well and sum (Inside, Outside) to equal -3. For this problem, those two numbers are -2 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 3y + 2
y² + (-2 - 1)y + (-2 x -1)
(y - 2)(y - 1)