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.

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 z° = 14, the value of a° is 14.

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.

-7c + 5 = 6 - 9c
-7c = 6 - 9c - 5
-7c + 9c = 6 - 5
2c = 1
c = \( \frac{1}{2} \)
c = \(\frac{1}{2}\)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(7ab) + (3a²)(7b)
(5 x 7)(a x a x b) + (3 x 7)(a² x b)
(35)(a¹⁺¹ x b) + (21)(a²b)
35a²b + 21a²b
56a²b

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.

8a - 8 > -3 - 2a
8a > -3 - 2a + 8
8a + 2a > -3 + 8
10a > 5
a > \( \frac{5}{10} \)
a > \(\frac{1}{2}\)