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 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 -63 as well and sum (Inside, Outside) to equal -2. For this problem, those two numbers are -9 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 2y - 63
y² + (-9 + 7)y + (-9 x 7)
(y - 9)(y + 7)

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

AD = AB + BD

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(4²) + 2π(4 x 6)
sa = 2π(16) + 2π(24)
sa = (2 x 16)π + (2 x 24)π
sa = 32π + 48π
sa = 80π

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.

4a - 4 = 3 - 2a
4a = 3 - 2a + 4
4a + 2a = 3 + 4
6a = 7
a = \( \frac{7}{6} \)
a = 1\(\frac{1}{6}\)