The Definition, Formula, and Problem Example of the Slope-Intercept Form
How To Rewrite An Equation In Slope Intercept Form – Among the many forms used to represent a linear equation, one of the most frequently found is the slope intercept form. It is possible to use the formula of the slope-intercept find a line equation assuming you have the slope of the straight line and the yintercept, which is the coordinate of the point’s y-axis where the y-axis is intersected by the line. Learn more about this particular line equation form below.
What Is The Slope Intercept Form?
There are three main forms of linear equations, namely the standard, slope-intercept, and point-slope. Although they may not yield the same results , when used in conjunction, you can obtain the information line that is produced more efficiently with the slope intercept form. It is a form that, as the name suggests, this form uses the sloped line and you can determine the “steepness” of the line reflects its value.
This formula can be utilized to determine a straight line’s slope, the y-intercept or x-intercept where you can utilize a variety formulas available. The line equation of this specific formula is y = mx + b. The straight line’s slope is symbolized through “m”, while its y-intercept is represented with “b”. Each point of the straight line can be represented using 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
In the real world, the slope intercept form is used frequently to show how an item or issue evolves over an elapsed time. The value of the vertical axis is a representation of how the equation deals with the magnitude of changes in the value provided by the horizontal axis (typically times).
One simple way to illustrate the use of this formula is to find out the rate at which population increases in a specific area as time passes. Using the assumption that the population of the area increases each year by a fixed amount, the point values of the horizontal axis increases one point at a moment each year and the value of the vertical axis is increased to reflect the increasing population by the fixed amount.
Also, you can note the starting point of a particular problem. The beginning value is located at the y-value in the y-intercept. The Y-intercept is the point at which x equals zero. If we take the example of a problem above, the starting value would be at the point when the population reading begins or when time tracking starts, as well as the changes that follow.
So, the y-intercept is the point at which the population begins to be monitored by the researcher. Let’s assume that the researcher is beginning to do the calculation or take measurements in the year 1995. Then the year 1995 will be considered to be the “base” year, and the x 0 points would occur in the year 1995. So, it is possible to say that the population in 1995 represents the “y”-intercept.
Linear equation problems that utilize straight-line formulas are almost always solved in this manner. The beginning value is represented by the yintercept and the rate of change is represented as the slope. The principal issue with the slope-intercept form generally lies in the horizontal interpretation of the variable in particular when the variable is accorded to the specific year (or any type in any kind of measurement). The most important thing to do is to ensure that you comprehend the meaning of the variables.