The Definition, Formula, and Problem Example of the Slope-Intercept Form
Linear Equations Slope Intercept Form – One of the numerous forms used to represent a linear equation the one most commonly encountered is the slope intercept form. The formula for the slope-intercept in order to find a line equation assuming that 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 fundamental forms of linear equations: standard, slope-intercept, and point-slope. Although they may not yield the same results , when used however, you can get the information line generated more efficiently with this slope-intercept form. As the name implies, this form employs an inclined line, in which the “steepness” of the line reflects its value.
This formula can be utilized to calculate the slope of a straight line, the y-intercept or x-intercept where you can apply different available formulas. The equation for a line using this particular formula is y = mx + b. The straight line’s slope is represented with “m”, while its y-intercept is signified via “b”. Every point on 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
When it comes to the actual world in the real world, the slope-intercept form is used frequently to depict how an object or problem changes in an elapsed time. The value provided by the vertical axis demonstrates how the equation deals with the extent of changes over the value provided via the horizontal axis (typically time).
One simple way to illustrate the use of this formula is to figure out the rate at which population increases in a certain area as time passes. If the area’s population grows annually by a predetermined amount, the value of the horizontal axis will increase by one point as each year passes, and the point values of the vertical axis will grow in proportion to the population growth by the set amount.
It is also possible to note the beginning point of a problem. The beginning value is at the y value in the yintercept. The Y-intercept is the place where x is zero. Based on the example of the above problem the starting point would be at the time the population reading begins or when time tracking begins along with the related changes.
This is the place where the population starts to be recorded by the researcher. Let’s assume that the researcher is beginning to do the calculation or take measurements in the year 1995. The year 1995 would be considered to be the “base” year, and the x = 0 points will be observed in 1995. This means that the population of 1995 is the y-intercept.
Linear equation problems that utilize straight-line formulas are nearly always solved this way. The starting value is depicted by the y-intercept and the change rate is represented through the slope. The most significant issue with this form typically lies in the interpretation of horizontal variables particularly when the variable is attributed to one particular year (or any type number of units). The trick to overcoming them is to make sure you know the variables’ meanings in detail.