MLS                                                                                       Yolanda Volcimus

Harvard                                                                              1/22/13

A percent is used to describe an amount of change in a number. There are numerous strategies that can be used to determine the percent of a number. In some cases, we can even find some real-world applications where percent is used. In addition, these real-world applications are necessary to have an understanding of the "story" behind the situation in order to apply the specific strategies. Therefore, there a various strategies that are involved in percentage.

       Percent of Change is the amount stated as percent; it is one of the strategies to determine the percent of a number. The two types of percent of change are percent increase and percent decrease. Percent increase is when the amount of a number improved; however, percent decrease is when the amount diminishes. The percent of change of a number is calculated as percent of change= amount of change over original amount. For example, in the statement "50 is decreased to 40", you would solve it by doing 50-40/50 based on the formula. Then, it would be 10/50 which is equal to 20%. Therefore, "50 is decreased to 40" is a 20% decreased. In addition, "25 is increased to 40" is a 37.5% increased because I set the problem as 40-25/40= 15/40= 0.375= 37.5%. That is to say, a strategy to find the percent of a number is percent of change.
       Furthermore, people can use discount which is a real-world application to find the percent of a number. Discount is a deduction from the original cost of an item. To find the discount of a number, we use the formula discount/original. It is necessary to have an understanding of the "story" behind the situation in order to apply the specific strategies because if we apply the wrong formula, we will end up with the incorrect percentage. For instant, if we have the story "At a store, an IPod was $50; however, it was on sale for 10% off. What was the new price?" If we have this problem, we know the strategy we would use is discount because 10% is being deducted from $50 and the new price would be $45.            

    Another strategy we can use to determine the percent of a number is commission. Commission is a free paid to a person who makes a sale. Commission is calculated by commission rate x sale = commission. In a real-world application, "A car is sale for $50,000 and Marvin gets 5% of this money? What is the commission?" Based on our understanding of the story, we know the correct strategy is commission because it is a free paid for Marvin. Marvin would receive $2,500 from the original amount.
     The last strategy we can use to find the percent of a number is revenue. Revenue is the amount of money brought in from a sale. After the costs are subtracted from the revenue, the amount remaining is the profit. For example, "the profit of 10 shirts was $50 which is 80% of the revenue. What is the revenue?" The revenue is $62.50 because I set a proportion of 80/100 = 50/x = 80x = 5,000= 5,000/80= 62.5.
        To wrap it all up, percent is an amount of change. The four strategies that are used to find the percent of a number are percent of change, discount, commission, and revenue. These strategies are all used in real-world application and the story is crucial in order to determine which strategy to use. In conclusion, the percentage of a number can be measures in many ways.

MLS                                                                                                    Yolanda Volcimus

Harvard                                                                                             January 10, 2013

For the last two months, I've been studying about linear equations. A linear equation is an equation between two variables that ends up in a straight line when it is graphed. I learned that there are three forms of linear equations; they are Standard Form, Slope-intercept Form, and Point-Slope Form. Each of these equations gave me specific information. That information provides a specific way for each equation form that changes my strategy for graphing. Also, there are situations where I find one equation form that is more useful than the others.

Standard Form equation is a linear equation that us written in the form of Ax+Bx =C. A, B, and C are all real numbers and A and B area not both equal to zero. To graph a linear equation in Standard Form, you can find the x-intercept by substituting zero for y and solving for x. To find the y-intercept, you must substitute zero for x. The information Standard Form equations provide is the y value when substituting zero for x and the x value when substituting zero for y. For instant, if I have this problem {3x + 4y = 12}, I would solve it like this:

Ax + By = C                                                     Ax + By = C    

3x + 4y = 12                                                   3x + 4y = 12

3 (0) + 4y =12                                                3y + 4 (0) = 12

4y=12                                                             3y = 12

4 = 4                    y=3                                      3  =   3                         y=4

This equation can be more useful than the other ones because this equation tells me the value of both x and y when finished solving it and I don’t even have to find the slope while the other equations give me other information except for the value of y and x. Therefore, Standard Form equations provide me with the value of y and x when I substitute zero for x and zero for y and this equation is useful because it provides the value of y and x.

Slope-Intercept Form equation is a linear equation that is written in the form of y= mx+b. The information this equation form provide is both the slope and the y-intercept. The m represents the slope {steepness of a line} of the line and the b is the y-intercept {on the y-axis, the value of x- is always zero}. In Slope-Intercept Form, the y-intercept tells me at what point to start at. Also, the slope tells me where the next point is located. For example, a graph have a y-intercept of 1 and a slope of 2 (Y= 2x + 1) . I can use this equation to find the y-intercept and the slope. The Y-intercept is 1 because the line crosses the y-axis at point 1 and the value of x- was zero. In addition, the slope is 2 because it was substituted from m to two. From point 1, since the slope is 2, you must move two places up and 1 place to the right {Y/X} = {2/1}. By using the slope and the y-intercept, it was easier for me to graph this equation without having to solve the entire equation. I can use this type of equation when I am given two points of a line, I use the slope formula {Y₂-Y₁ / X₂ –X₁} formula this equation to write the equation of a line. Therefore, Slope-Intercept Form equations give me information like the slope and the y-intercept. 

      Point-Slope Form equation is a type of equation that is according to the slope and a point of a line. The information that this equation provide is the slope and the point of the line. The general equation for this form is Y-Y₁= m (X-X₁). Y₁ must be the opposite, m is the slope, and X₁ must also be opposite. For instant, the point of a line is (5, 15) and the slope is 3. I would write this information into point-slope form equation by first using the formula Y-Y₁= m (X-X₁). Then, I would substitute for the y, the slope, and the x in the equation{y-15=3(x-5)}. Therefore, the final equation in Point-Slope Form is y-15=3(x-5). When graphing, I can use this equation because this equation provide us with the slope and the specific point. When a problem only gives me one point of the line and the slope, the equation that is useful to use is this equation because this equation is the only equation I can use when I am given any point of a line with the slope. That is to say, when only given one point of a line and the slope, I can use the Point-Slope form equation to figure out the next point. 

        To wrap it all up, I learned that a linear equation is an equation that provides a straight line when it is graphed. I learned about the three types of linear equations which are Standard Form, Slope-intercept Form, and Point-Slope Form. Each type of equation gives a specific type of information that is unique in order for me to graph it. In addition, there are situations where one equation form is more useful than the other. In conclusion, I can use any of these equations to graph a straight line because they are all linear equations.