Term Paper: Tag Members of a Population

Pages: 2 (733 words)  ·  Bibliography Sources: 0  ·  Level: College Junior  ·  Topic: Education - Mathematics  ·  Buy This Paper


[. . .] The assignment is to solve for y and identity the type of equation that results when solving for y. The number sentence given is: y-1/x+3 = -3/4. Using cross multiplication gets rid of the denominators and yields the following equation: 4(y-1) = -3(x+3). The goal is then to isolate y on the left side of the equation, which gives one an equation solving for y. Without additional information, the equation cannot be solved for either the numerical value of x or y because doing so requires multiple equations or providing what x or y is. This information suggests immediately that the equation represents not a single set of coordinates, but a line. As a result, one is already thinking that the end-result of the process will be an equation for a line. The slope, intercept form of an equation for a line is popularly represented as y=mx + b where m represents the slope of the line and b represents the y intercept of the line. (The y intercept is the point on the line where it intercepts the y axis; in other words, the y intercept is the point on the line where x=0). Knowing this basic form of an equation helps guide the shaping of the equation as one solves for y.

The first step is to multiply each side of the equation. 4(y-1) becomes 4y-4. -3(x+3) becomes -3x -9. The equation them comes 4y-4 = -3x -9. The next thing to do is to add 4 to both sides as the next step in isolating y. The resulting equation is 4y= -3x -9 + 4 or 4y=-3x-5. One then divides both sides by 4 to continue isolating y. The resulting equation is y=(-3x-5)/4. The four is distributed throughout the equation, yielding the following equation y=-3/4x -5/4. That equation is an equation for a line with the slope -3/4 and a y intercept of -5/4. The y intercept provides the solver with a set of numbers that can be applied to the equation (0,-5/4). Plugging these numbers back into the equation allows one to eliminate the possibility of an extraneous response. y-1/x+3 = -3/4. Does (-5/4- 1) / 3 = -3/4? -5/4-4/4=… [END OF PREVIEW]

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