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.

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with x° = 165, the value of c° is 15.

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 equal sign and the answer on the other.

-5b - 4 = \( \frac{b}{-9} \)
-9 x (-5b - 4) = b
(-9 x -5b) + (-9 x -4) = b
45b + 36 = b
45b + 36 - b = 0
45b - b = -36
44b = -36
b = \( \frac{-36}{44} \)
b = -\(\frac{9}{11}\)

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 equal sign and the answer on the other.

7x + 9 = 6 + 9x
7x = 6 + 9x - 9
7x - 9x = 6 - 9
-2x = -3
x = \( \frac{-3}{-2} \)
x = 1\(\frac{1}{2}\)