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A linear function has four possible types of slope:
- Positive – This slope is reflected on the graph as a line rising from left to right. In this case, m>0 .
- Negative : the graph of the line descends from the left to the right. On these slopes, m<0 .
- Null : in this type of slope no angle is formed. That is, if we draw a line on a Cartesian plane, any line that is parallel to the “x” axis will be horizontal, and therefore its slope is zero: m=0 .
- Undefined : when the line is vertical, parallel to the « y » axis, the slope is undetermined, that is, it cannot be defined.
The negative slope: definition
The slope, then, would be the difference of the « y » axis divided by the difference in the « x » axis for two different points on a line. It is usually expressed as an absolute value. A positive value indicates a positive slope, while a negative value indicates a negative slope. For example, in the function y = 5 x , the slope is positive 5; therefore, it is a positive slope.
The slope is negative when the angle that the line forms with the positive part of the axis is obtuse. Stated another way, negative slope can be defined as the steepness of a line that demonstrates a decline from left to right. For example: if y = -x + 2, this means that it has a negative slope of -1.
Negative Slope and Negative Correlation
Furthermore, the negative slope represents a negative correlation between two variables. This means that as one variable decreases, the other increases, and vice versa. Negative correlation represents a significant relationship between the variables « x » and « y «. Depending on what it is representing, it can be understood as input, output, cause or effect.
Negative correlation occurs when the two variables in a function move in opposite directions. For example, as the value of ” x ” increases, the value of ” y ” decreases. And when the value of “x” decreases, that of “y” increases.
In a scientific experiment, a negative correlation would show that an increase in the independent variable causes a decrease in the dependent variable. Using this feature, a scientist could show that as predators are introduced into a habitat, the number of prey decreases.
How to calculate the negative slope?
The negative slope is calculated by dividing the elevation of two points, that is, the difference along the vertical axis and the difference along the x-axis. The negative slope formula can be expressed as follows:
m = (y2 – y1) / (x2 – x1)
When plotting the line on the graph, the slope will be negative if the line falls from left to right. It is even possible to know if the slope is negative simply by calculating « m «. For example, if we calculate the slope of a line containing the two points (7, -1) and (1,1), using the given formula, we will get the following data:
m = [1 – (-1)] / (1-7)
m = (1 + 1) / – 6
m = 2 / -6
m = – 3
Here the negative slope of -3. This means that for every positive change in x , there will be three times as many negative changes in y .
Examples of negative slope
The concept of negative slope can be applied in everyday life. For example:
- When going down a mountain, the further down you go, the further down you will go. This can be represented as a mathematical function where y is the elevation and x is the distance traveled.
- Juan has more and more expenses and, therefore, less money in his bank account.
- Maria has an exam but she can’t concentrate. The more time she spends distracted without studying, the lower her test score will be.
- When flying by plane, the higher the altitude, the lower the atmospheric pressure.
Bibliography
- Everitt, BS The Cambridge Dictionary of Statistics (2002, 2nd ed.). Spain. Cambridge University Press.
- Martínez Bencardino, C. Basic applied statistics (2016, 4th edition). Spain. Ecoe Editions.
- Juárez Hernández, LG Practical manual of basic statistics for research (2018). Spain. K Research Corp.
