Understanding what is slope intercept form
Mathematics, particularly algebra is considered to be one of the most difficult disciplines to study. As a rule, students spend huge amounts of time to learn all the theorems, definitions and other mathematical issues, although some of the issues are still hard to comprehend. One of the most popular difficulties that students face during their studies on mathematics is comprehending of what is slope intercept form. As a rule, algebraic linear equations are an essential part of mathematical course during the studies in a high school. One of the forms that algebraic equations can take is a slope intercept form, which explains the importance of knowing and understanding what is slope intercept form. Even though there is a wide range of books on mathematics and online resources where the students can find the explanation of what is slope intercept form, the majority of them are not really helpful, because they provide the information in a complicated form that is hard for perception, especially if mathematics is not your biggest strength. In this article, you will find out a lot of interesting and helpful information that will ease your studying of mathematics, particularly algebra, and also, you will find a clear and understandable explanation of what is slope intercept form, how to deal with it and how to solve algebra problems referring to this issue.
In order to have a clear image of what is slope intercept form, you need to know first of all, that it has to do directly with algebraic equations of a line. All the existing actual and potential algebraic equations of a line can take a number of forms. They may look absolutely differently at first sight, although all of them have similar purpose, they serve for the same goal and are used within solving the same algebraic problems. The purpose which algebraic equations of a line serve for, is describing a line. In other words, all of the algebraic equations can describe the same line, although the way of the description can be rather different. More than that, the algebraic equations themselves can be absolutely equivalent, although visually they may differ one from another significantly. The first and the most common form, which an algebraic linear equation can take is the slope intercept form. Therefore, if you are asked what is slope intercept form the first thing you need to answer is that this is the form that all the algebraic linear equations usually take and you will not be mistaken.
Having said that, not only to know what is slope intercept form is important, but also to know how to write an algebraic equation in this form. As a rule, assignments on algebra require writing a linear equation in this form. So if you need to deal with this kind of task, the first thing you need to do is to select two points on the given line and with the help of these two points, to find the slope. The slope will be the value of m (which determines the slope in the equation). After that, you will have to look for the coordinates of the y-intercept. Here, you will deal with the value of b (which determines the y-coordinate of the selected point where the line intercepts the y-axis). In the end, you will have to write the algebraic linear equation using the data that you received by means of the above-mentioned operations. At the end of the day, we recommend you checking your equation and making sure your answer is correct. You can do this by selecting a particular point on the given line (keep in mind, however, that this line should not be within the y-intercept) and entering it into the equation in order to figure out whether it satisfies the algebraic equation or not. If it satisfies the equation, it means that you have solved the algebra problem and your answer is correct.
Getting familiar with the slope
Apart from what we have already said, it is important to mention that the understanding of what is slope intercept form is impossible without understanding what is a slope itself. Therefore, let us enlighten the term «slope» and find out its definition and common usage.
In terms of mathematics, the slope (which is sometimes also called «gradient») of the given line represents the number describing what kind of direction and steepness are peculiar to that or another line. As a rule, when writing or speaking about the slope, they use the letter «m». It is hard to determine the reason of why it has to be m, not some other letter, but it doesn’t really matter, since such denoting of a slope is commonly accepted all over the world. Some scientists in the area of mathematics argue that there can be only one explanation of using the letter «m» to determine the slope. They say that m determines the such a word as «multiple».
As for the direction of the line, it can be of different kinds, such as vertical, horizontal, increasing or decreasing. In order to determine of what kind the direction of that or another line is, you need to figure out whether the line goes up or whether it goes down; whether the line is horizontal (which means that you deal with a constant function and the slope is 0) or whether the line is vertical (which means that the slope cannot be defined and it is called «undefined» in such cases).
As for the steepness of the given line, you can also determine it on your own. In order to do this, you need to use the absolute value of the given slope. An absolute value, in terms of mathematics, including algebra as a branch of it, is the non-negative value of the x, without referring to the sign of x. When you have found the slope, you will have to figure out the greater absolute value, since the greater absolute value shows that the line is a steeper.
What is a linear equation
To know and understand what is slope and what is slope intercept form requires also understanding of such an issue as an algebraic linear equation. This kind of an equation is characterized by the fact that every term in it remains a constant or at least represents the product of the constant, as well as a single variable (this is a particular alphabetic character indicating certain number, which is usually unknown or requires further investigation). Constants can be of different forms, including but not limited to the numbers, different parameters, various functions (even such as non-linear functions) of parameters. All kinds of algebraic linear equations can have either one or more than one variables. Problems referring to the linear equations occur in most of the branches and areas of the study of mathematics, but primarily in the applied mathematics, which is a specific branch dealing with mathematical methods used in science (including computer science), engineering, different areas of business and even industry. Such a broad usage of linear equations explains why it is so important to understand this issue and to be able to cope with it, since nobody knows what future life has prepared for you. Quite possibly you will get involved in one of the spheres where linear equations are quite a popular occurrence.
When studying linear equations in the high school, students only get familiar with the essentials of this issue. On the other hand, basic knowledge about linear equations is enough to determine whether you are interested in this issue or not. In any case, dealing with this topic of mathematics is useful, since it will improve your analytical and logical skills.
Learning to use the slope intercept form in algebra
Now that you know what is slope intercept form, it would be good to learn how to use the slope intercept form in algebra. As we have already said, this is a commonly accepted method to present an algebraic linear equation. Guidelines provided below explain the methodology of the usage of the intercept form. Read them carefully and follow them when dealing with the assignment on algebra concerning this issue.
- First of all, read the algebra problem provided in the assignment. Before you actually proceed to solving the problem, you have to read attentively the problem in order to comprehend what exactly you are required to do. For example, you may be asked to find the way to represent the relationship between the earned money and the amount of time of working by means of slope-intercept form.
- The next step you need to undertake is to analyze the algebra problem in the light of the slope-intercept form. You have to write down the formula y=mx+b, where every symbol has its specific meaning: the m represents the change, the b indicates the starting point. By the starting point, we mean the point where the given line comes through the y-axis.
- After that, you need to search the slope of the given line. In order to cope with this task, you need to find the rate of the change. In terms of the question provided in the example, you will have to determine the sum that you started to work with and figure out what sum you had after working for a defined period of time.
- The next step is to find the y-intercept. In order to deal with it, you have to search for the starting point of the assigned problem, which means to figure out where it comes through the vertical axis. You have to know the precise sum of money that you started to work with.
- Now that you have the equation, you need to write it down in the slope-intercept form.
- Check you equation. The y has to indicate the overall sum of money that you have earned and the x has to indicate the overall sum of money that you have earned within the given period of time.
- Plug in a different number indicating the given amount of time into the equation in order to find out the sum of money that you have earned within this period.
This is one of the possible methodologies to apply the slope intercept form. Apart from it, there is also another method, based on the equation to the slope intercept form. Keep reading to learn how to use this method.
- At first, you need to separate the y-term and put it on the one side of the equation. Here, all you have to do is to move the x to the other side in such a manner that the y stays by itself. Keep in mind that moving of a term (whether by means of adding, subtracting, etc.) to the opposite side of the algebraic equation, you need to change the signs. This means that the positive sign has to become negative and the negative sign has to become positive.
- Now you need to divide all the terms that you have in your equation by the y-coefficient. This coefficient indicates the number located in front of the y. There can be a situation, when there is no coefficient in front of the y term. If this happens, it means that you’re finished. But in case if there is a coefficient, you have to divide every term in your algebraic equation by the number indicated by the coefficient.
- Now you need to determine the terms in the equation. In case if you use it for plotting a line, remember that x serves to indicate the x-coordinate, while y serves to indicate the y-coordinate.
Be aware that if you undertake all the steps without taking notes and you do all the operation in your mind, this may lead you to various difficulties as a result. A better way is to see everything written on a piece of paper, because it will help you be more concentrated and not to get lost in the order of the steps and in the data that you get from coping with each operation. Take into consideration that you can always use professional custom paperwriting service, whether you need to complete assignment on algebra or any other discipline
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