It is essential to know how a straight line angles from the horizontal and that is called the ‘slope’ of a line. It is also defined as the rise over run. If m is the slope, the formula can be written as m = rise/run.
How To find the Slope of a Line?
It is essential to know if the line is straight or not as the slope can be found only for a straight line. On a graph, if the coordinates are x and y which is represented as (x,y). There have to be two points that need to be picked which are different but are on the same line. Next thing to pick is the point which s dominant and remains the same all through the coordinates. Consider the dominant coordinates to be x1 and y1, and the other coordinates are x2 and y2.
The equation will have y coordinates on the top and x on the bottom. Find the difference of the two points in the y coordinates, y2-y1 and subtract the x coordinates from one another x2-x1. Divide the y coordinates by the x coordinates to get the slope.
m = 2−1/2−1
Cross-check the result obtained through visual analysis.
Lines that traverse up from left to right even if they are fractions are positive numbers and the lines that drop down from left to right even if they are fractions are negative numbers.
How to Find the Slope of a Single Point?
Finding the slope of a line with only one point is not possible if you have a graphical representation available like a graph, then a second point can be found and the formula for slope m = (y2-y1) / (x2-x1).
If a single point is given on an XY graph, a random point can be chosen from the infinite points available so that a line can be drawn and slope determined. So for one point, there can be n number of slopes and having only one point it is not enough to find the slope of a line without the help of a graph or table handy.
Moreover, slopes are calculated taking into consideration change in y coordinates and dividing it by the difference in x coordinates of two points in a graph. Since for a single point, there can be ‘n’ number of lines crossing you cannot determine the slope of a line without having a second point.
A real-life example of slope:
It can be used to determine how the savings account is increased over a period. To find the rate at which the amount in the account has increased, you can use the formula (y2-y1)/(x2-x1). If the initial amount was o and is now $1200 at the end of the year, then the rate of change in amount is (1200-0)/(12-0) = 1200/12 = $100 per month.
Other examples can be driving a car on a slope, trekking on a mountain, skiing downslope, calculating the incline in a bridge, a job where you get paid commission on selling ‘n’ number of cars and much more. We can find the growth of a tree at a constant rate over a period of time through a graph by interpreting the slope of the line on the graph.
Understanding the concept of slope is essential as it helps to measure the rate at which changes take place.