The Definition, Formula, and Problem Example of the Slope-Intercept Form
Slope Intercept Form (y=mx+b) – What is Slope Intercept Form? – Among the many forms used to represent a linear equation, one of the most commonly found 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, which is the point’s y-coordinate where the y-axis is intersected by the line. Read more about this particular linear equation form below.
What Is The Slope Intercept Form?
There are three basic forms of linear equations: the standard, slope-intercept, and point-slope. Even though they can provide the same results when utilized, you can extract the information line produced more quickly by using the slope-intercept form. As the name implies, this form uses a sloped line in which the “steepness” of the line reflects its value.
This formula can be used to discover a straight line’s slope, y-intercept, or x-intercept, where you can apply different available formulas. The line equation of this specific formula is y = mx + b. The straight line’s slope is signified by “m”, while its y-intercept is signified by “b”. Each point of the straight line is represented by an (x, y). Note that in the y = mx + b equation formula, the “x” and the “y” have to remain as variables.
An Example of Applied Slope Intercept Form in Problems
In the real world, the slope intercept form is often utilized to represent how an item or problem changes in the course of time. The value provided by the vertical axis represents how the equation deals with the intensity of changes over the value provided by the horizontal axis (typically time).
A simple example of this formula’s utilization is to find out how the population grows in a certain area as the years pass by. Using the assumption that the area’s population increases yearly by a specific fixed amount, the point value of the horizontal axis will increase one point at a time for every passing year, and the point value of the vertical axis will increase to represent the growing population by the fixed amount.
You can also note the starting value of a problem. The starting value occurs at the y-value in the y-intercept. The Y-intercept is the point at which x equals zero. By using the example of a problem above, the starting value would be when the population reading begins or when the time tracking begins along with the related changes.
So, the y-intercept is the point in the population where the population starts to be recorded by the researcher. Let’s say that the researcher begins to do the calculation or the measurement in the year 1995. Then the year 1995 will be the “base” year, and the x = 0 points would occur in the year 1995. Therefore, you can say that the population in 1995 is the y-intercept.
Linear equation problems that use straight-line formulas are nearly always solved this way. The starting value is represented by the y-intercept, and the rate of change is represented by the slope. The primary complication of the slope intercept form typically lies in the horizontal variable interpretation, particularly if the variable is accorded to a specific year (or any type of unit). The key to solving them is to ensure that you understand the variables’ definitions clearly.