The slope formula is one of those sections in the algebraic mathematics that the student found very hard to master. We have introduced this article so that the students in the stream of mathematics could simplify the studying process of the equation of the line and slope formula. This article on Slope Formula is purely aimed at the academic augmentation of the students. Before the drafting process of this article on slope formula, we have conducted and implied the model of Jigsaw II and emotional intelligence. The samples were selected from 5 different colleges by the method of random cluster sampling. While the evaluation of these data we have observed that emotional intelligence and other learning models have no significance in the process of learning the slope formula. Just sustaining the level of happiness and factor of interest in the student would simplify the whole process. We have intended this article for our students who have repeatedly asked a genuine way to master the slope formula.
The branch of mathematics is now well developed and a lot of research has done by many of the scholars in the respective branches. Though the scholars and other scientists have not lost interest in the science of mathematics and the trend of conducting different researches in the interesting field is increasing day by day. The scope of mathematics could not be measured, similar is the case with its subdivision of algebra. In the stream of algebra, the numbers to be used in the arithmetic expression could be denoted by using the alphabetical denotations. There would be no change in the rules to be followed in the arithmetic expression. It is the branch of algebra that has contributed much more to the evolution of mathematics to the modern form. Hence the section of algebra should be taken very seriously by the students how have adopted mathematics as their core academic course.
While considering the learning stage of algebra, various theories and concepts should be taken into account of which most of them are in the form of equations. Even the section of the equation is being divided into various sections like straight-line equations, differential equations, polynomial equations, linear equations, two variable equations, etc. Of these divisions, some of the equations may appear to be a very easy one to be solved through some may appear very challenging to solve. As per the complexities and the toughness level of the equation, the solutions are being distributed accordingly in the courses of high schools and colleges. These equations not only entail significance in the course of mathematics but also other sub-branches of the science.
It is a minor section of the mathematics that entails the section of algebra and the related equations. The related section contains major theory and ideologies like line equation, theories associated with lines, perpendicular and parallel lines, slope formula of line, and other equations related to the straight line. The students in Asian countries like Indonesia have included this chapter in the early educational stages of high school. The topics like the equation of straight lines, slopes, quadratic equations, etc. still possess a lot of significance in the current educational stream.
In the curriculum of mathematics, the functions entail a lot of significance. In the study and the research of the linear function, the concept of slope plays a very crucial role. The concept of the slope had also increased and encroached its scope to advanced algebra. Simon and Blume in their research have found it that the students have found it very difficult to study the concepts of both physical and functional problems. Through various surveys and evaluations are done by the government bodies, the response of the students in the related field was evaluated. By the respective survey done by us, it was observed that only around 51 % of the students have mastered the concept of slope formula. This is a very considerably low percentage and signifies that the students have a very little grasp over the slope formula some innovative measures should be implied for the oversimplification of the whole process. The issue should be taken very seriously by the teachers and the tutors otherwise the students would miss a very crucial part of the mathematics. Since the course of algebra is changing day by day, the students should be made aware of the basic algebraic ideologies and theories on an urgent basis. Various measures should be taken to increase the skills of the students is the alteration and augmentation of the learning processes in academic institutes. It is majorly observed that the process and the style of teaching adopted by the teacher would impact most on the learning ability of the student. We have understood that only by adopting an innovative measure the theory of slope formula and its information could be taught to the student. While studying the slope formula himself by the student, he should use a very innovative method to heart it. The major methodologies used by the lecturers all over the world for teaching the slope formula is by Teams Games Tournament and Jigsaw II.
Straight line and slope formula
If a graph is being created by joining the points whose numerical values would satisfy the slope formula. The adjoined form of these points would graphically represent a straight line with a considerable slope. Below is provided with the generic formula for the straight-line equation.
Ax + By + C = 0
The variables A, B, and C represent the real numbers. The equation represents the points through which the straight-line passes. Normally the straight line is created by adjoining two separate points. To get the coordinates for the point which would satisfy the above-given equation, the below-given formula could be used.
(x – x1) (y2 – y1) = (y – y1) (x2 – x1)
The obtained coordinates would be in the form of (x1, y1) and (x2, y2), through which the straight line would pass.
If the taken instance of any straight line, it processes some numerical value of the slope. The rate of change of the numerical value of y concerning its coordinate could be represented or indicated as the slope of the selected straight line. The slope of the elected straight line would be indicated y the variable m. It is by taking into account the two points of the straight line that the slopes are calculated. The slope could be calculated by using the generic formula as provided in the below section.
M = (variation in the value of y)/ (variation in the value of x) = ∆y/∆x
The symbol of ∆ which is a Greek letter (spelled as delta) signifies the change in numerical value or other dimensions. In other words, it denotes the change in the magnitude of the selected variable. The general or the empirical formula could be denoted as in the below form.
Y = mx + c
C represents the numerical value of the coordinates with respect to the Y-axis. The whole ideology would be to draft the geometrical figures while satisfying the rules of cartesian rules. Either the lines would get crossed or show the parallel characteristics if displayed on a two-dimensional plane. By looking at the value of the slope, it could be mentioned that whether the lines are perpendicular or parallel to each other. If the selected set of line segments possesses the same value of the slope, then it could be implied that they are parallel to each other. The case in which the product of the numerical values of slops turns out to be -1, it could be deduced that the taken lines are perpendicular to each other.
In most of the countries, the slope formula is introduced to the students in the stage of high school (class 8). Before entering into the learning process of slope formula, the student should have mastered the laws and theories of algebra. If the student has no skills in solving the linear equations or inequalities, mastering the slope formula would be much difficult for him. Only if the student has got his proper education of mathematics in the lower secondary graduation, he should go through the ideologies of the slope formula. The complex nature and the scope of implementation of the slope formula would considerably increase while student starts his university graduation. If the student is intending to learn the slope formula, he should stick throughout the generic forms and less complex form of slope formula. The formula is majorly limited to the two-dimensional figures.
Because of the abstract nature of algebra, a student may require a considerable amount of time to master the slope formula. Hence the students should have appropriate guidance and perseverance to deal with the various variants and implications of the slope formula. You could continue by adopting various modes of learning and practice sheets for implying an effective way of studying it. In the initial stage, the student should try drawing straight lines on the cartesian graph paper. The practice should be done by keeping in mind the coordinate position of the relevant points. While you get comfortable with it, go on with calculating the slope of the drawn line segment. While pursuing this process, go on with finding which lines are perpendicular or parallel to each other. The numerical value of slope would be very crucial while sorting out the drawn line segments. In the latest stage, the student should take as many examples from the worksheets.
Only the conceptual knowledge regarding the slope formula would help the student in mastering the whole theory. The various derivations and the reason behind the evolution of the equation should be understood by the student to get a thorough conceptual knowledge of the slope formula. The practical knowledge integrated with the conceptual knowledge would help the student in attaining higher academic grades. It has been observed in many graduates that they are implying the slope of formula in the practical world in a very wrong way because of the lack of conceptual knowledge of algebra. Unless the student would master the basics of algebra, studying the concepts of slope formula would be very hard for the mathematic student. Don’t keep yourselves away from the slope formula if you find it very hard to follow as the major chunk of the mathematic stream would deal with the implementation of the slope formula. The covariational reasoning could also be augmented with respect to the student if the lessons regarding the slope formula are mastered by him. Without covariational reasoning, a student could not pursue his higher education in the field of mathematics. The development of covariational reasoning in a person could be depicted in the three gradual stages. Which are acquiring the senses of Coordination, Direction, and at last having the knowledge regarding the implementation of quantitative coordinates?
We know that the same theory could be conceptualized in a very different and unique way by each student. Though it would be a little hard for students with limited academic and reasoning ability.
Roughly saying, the slope formula is used to find the inclination of the line segment with respect to the horizontal (either x-axis or the y-axis). They are used generally to analyze or to predict the future course of a curve. The concept of slope formula could be related to the angular coefficient or that of the ideologies of the tangent. The slope is considered to be the equivalent of the derivative of the selected function. The value of the function would be directly proportional to the numerical value of the slope. The variable m in the equation y = mx + b signifies the numerical value of the tangent of an angle. M is the variable is the ratio of change in the magnitude of y coordinate with respect to the change in the magnitude of the x coordinate. Higher the value of the variable m would get, steeper the selected straight line would get with respect to the opposite coordinate.