When dealing with linear equations, one of the most important pieces of information to determine is the slope of the line. The slope describes the steepness of the line and how quickly it is increasing or decreasing. The formula for finding the slope of a line passing through two points, (x1,y1) and (x2,y2), is:
slope = (y2 – y1) / (x2 – x1)
In this article, we will explore how to find the slope of a line passing through two given points, specifically the points m(1,3) and n(5,0).
Step 1: Identify the Coordinates
To start the process of finding the slope of the line, we need to first identify the coordinates of the two points in question. In this case, we are given the two points: m(1,3) and n(5,0).
Step 2: Plug in the Coordinates into the Slope Formula
Next, we will plug the coordinates into the slope formula in order to calculate the slope of the line. Using the formula, we get:
slope = (y2 – y1) / (x2 – x1)
slope = (0 – 3) / (5 – 1)
slope = -3/4
Therefore, the slope of the line passing through the points m(1,3) and n(5,0) is -3/4.
To better understand what this slope means, let’s take a look at some characteristics of lines with different slopes.
Lines with Positive Slopes
A line with a positive slope increases as we move from left to right. The steeper the line, the larger the slope. For example, a line with a slope of 2 would be steeper than a line with a slope of 1. Additionally, if the slope is greater than 1, the line is considered to have a steep positive slope.
Lines with Negative Slopes
A line with a negative slope decreases as we move from left to right. The steeper the line, the smaller the slope in absolute value. For example, a line with a slope of -2 would be steeper than a line with a slope of -1. Additionally, if the slope is less than -1, the line is considered to have a steep negative slope.
Lines with Zero Slopes
A line with a slope of 0 is a horizontal line. It does not increase or decrease as we move from left to right.
Lines with Undefined Slopes
A line with an undefined slope is a vertical line. It goes straight up and down and does not have a slope in the traditional sense.
Conclusion
To summarize, finding the slope of a line passing through two points is a crucial step in understanding linear equations. By using the formula (y2 – y1) / (x2 – x1), we can easily calculate the slope of the line and determine its characteristics, such as whether it has a positive or negative slope or if it is horizontal or vertical. So, the next time you encounter a linear equation, remember to find the slope first and solve from there!
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