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.