The Definition, Formula, and Problem Example of the Slope-Intercept Form
Writing Equation In Slope Intercept Form – One of the many forms employed to depict a linear equation, among the ones most commonly encountered is the slope intercept form. You may use the formula of the slope-intercept to find a line equation assuming you have the straight line’s slope , and the y-intercept. This is the point’s y-coordinate at which the y-axis crosses the line. Learn more about this specific line equation form below.
What Is The Slope Intercept Form?
There are three fundamental forms of linear equations: the traditional, slope-intercept, and point-slope. While they all provide similar results when used but you are able to extract the information line generated faster by using the slope intercept form. As the name implies, this form employs a sloped line in which the “steepness” of the line indicates its value.
The formula can be used to discover a straight line’s slope, the y-intercept, also known as x-intercept in which case you can use a variety of formulas that are available. The line equation of this specific formula is y = mx + b. The straight line’s slope is signified in the form of “m”, while its y-intercept is indicated with “b”. Each point of the straight line is represented with an (x, y). Note that in the y = mx + b equation formula the “x” and the “y” are treated as variables.
An Example of Applied Slope Intercept Form in Problems
The real-world, the slope intercept form is frequently used to depict how an object or issue changes over it’s course. The value provided by the vertical axis indicates how the equation addresses the degree of change over what is represented with the horizontal line (typically times).
A basic example of using this formula is to discover how much population growth occurs in a specific area as the years pass by. Based on the assumption that the area’s population increases yearly by a fixed amount, the point value of the horizontal axis will rise by one point with each passing year and the point values of the vertical axis will rise in proportion to the population growth by the fixed amount.
Also, you can note the starting value of a problem. The beginning value is at the y-value in the y-intercept. The Y-intercept is the point where x is zero. In the case of the above problem the beginning point could be at the time the population reading begins or when the time tracking starts along with the changes that follow.
This is the point when the population is beginning to be monitored in the research. Let’s suppose that the researcher is beginning to calculate or measurement in the year 1995. The year 1995 would become the “base” year, and the x = 0 points would be in 1995. This means that the 1995 population will be the “y-intercept.
Linear equation problems that utilize straight-line formulas are almost always solved in this manner. The starting point is represented by the y-intercept, and the rate of change is expressed through the slope. The primary complication of this form generally lies in the horizontal variable interpretation especially if the variable is associated with the specific year (or any other kind of unit). The trick to overcoming them is to make sure you are aware of the definitions of variables clearly.