Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and 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°).

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

3a - 4z = -4a - 8z + 7
3a = -4a - 8z + 7 + 4z
3a + 4a = -8z + 7 + 4z
7a = -4z + 7
a = \( \frac{-4z + 7}{7} \)
a = \( \frac{-4z}{7} \) + \( \frac{7}{7} \)
a = -\(\frac{4}{7}\)z + 1

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, 3) and (2, 5) so the slope becomes:

The coordinate grid is composed of a horizontal x-axis and a vertical y-axis. The center of the grid, where the x-axis and y-axis meet, is called the origin.

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 -45 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -9 and 5. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 4y - 45
y² + (-9 + 5)y + (-9 x 5)
(y - 9)(y + 5)