Equation Examples Solving Linear Equations subtract divide by Solving Linear Equations (including fractions) (1/2)x = 4 + x multiply by (2/1) or x = 8 + 2x subtract subtract x -8 = x, or x = -8 Solving Inequalities 4x > divide by Intro to Functions f (x) = 7x + 9 evaluate for x = 3 solve arithmetic f (3) = 30 Finding Slope A line passes through (-5, 7) and (10, 17) Find the rise (y2 -- y1) Find the run (x2 -- x1) Slope = rise/run Finding the Equation

equations for a macroeconomic model including private, public, and international sectors. Derive the aggregate demand function. List the forces (i.e., factors) which are held constant for each behavioral equation. Select four of these and, for each, explain how a change in the exogenous factor will affect the aggregate demand function. Explain the effect of each change on real income and output, employment, the price level, the interest rate, the

8 meters/s^2), and t is the time elapsed in seconds. For example, an object is thrown at 9 meters per second. The path it will travel is described by the following graph: 3.Hyperbola Hyperbolas are produced using equations of the form (x - h)^2/a^2 - (y - k)^2/b^2 = 1. There are various examples of hyperbolas in real-life. Two stones thrown in a pool of water will produce ripples of concentric circles.

relationship pass the vertical line test, for being a function? What is its range? What is its domain? What are its X-intercepts, if any? (3,0) (6,0) What is its Y-intercept, if any? What is the nature of the relationship (linear, quadratic, etc.)? nonlinear and nonquadratic What is the value of f (x) at x=-2? (3) Does the relationship pass the vertical line test, for being a function? What is its approximate range? What is its approximate domain? What are its X-intercepts,

Thus, in 1 Kings 7:23, the word "line" is written Kuf Vov Heh, but the Heh does not need to be there, and is not pronounced. With the extra letter, the word has a value of 111, but without it, the value is 106. (Kuf=100, Vov=6, Heh=5). The ratio of pi to 3 is very close to the ratio of 111 to 106. In other words, pi/3 = 111/106

Drug Wars A Thin, Bloody Line Borders are artificial lines. Even when they follow natural divisions such as rivers or mountain ranges, borders are still artificial. They are imaginary lines that different governments (or other official groups of people) have decided marks the place on the earth where the authority and power of one group ends and the power and authority of the next group begins. Borders are in general a good idea