Slope of a line is the measure of the inclination of the line. The slope of a line can be calculated easily and it gives important information regarding the line. The slope of the line tells us whether a line is moving upwards or downwards. It also tells us how steep the inclination of the line is. This article on how to calculate slope of a line will help you in calculating slope.
Calculating slope of a line
Follow the steps below to calculate slope of a line:
A line is usually a set of individual points. You can calculate the slope of the line drawn on the graph paper by locating its x and y coordinates.
Slope of a line is given by the formula
Slope = Y2 – Y1
X2 – X1
- Y2 – Y1 is called the rise of the slope which is also denoted as ∆ Y
- X2 – X1 is called the run of the slope which is also denoted as ∆ X
Step 1: Each line has an x-axis value and a y-axis value. Suppose the line passes through the points (1, 2) and (2, 5)
Step 2: Here,
Y2= 5 and Y1= 2
Calculate rise of the slope
Rise = Y2 – Y1
Rise = 5 – 2
Therefore,
Rise = 3
Step 3: The values of X2 and X1 are
X2 = 2 and X1= 1
Calculate run of the slope
Run = X2 – X1
Run = 2-1
Run = 1
Step 4: Calculating slope of the line. As slope of the line is the ratio of rise and run of the slope,
Slope = Rise = ∆Y
Run ∆X
Therefore,
Slope = 3/1 = 3
- If you have been given the equation of line as y= (2/3) x – 4, then to calculate slope of the line you need to place some arbitrary values for x and y in the equation.
- Initially, place some arbitrary values for x and find out the values of y. Similarly, place some arbitrary values for y and find out the values of x.
- Draw the line on the graph paper and select any two points on the line. Locate the x and y coordinates of these points and follow the steps 1 to 4 given above to find out the slope of the line.
You can also determine the nature of the slope when you have calculated the slope of the line.
- If the slope of the line is positive, then the line is moving upwards.
- If the slope of the line is negative, then the line is moving downwards.
- More is the number, steeper is the line. This means that a line with slope 4 is steeper than a line with slope 3.
- The slope of the horizontal line or the line which is parallel to x-axis is neither negative nor positive. Slope of such a line is zero as it is neither going upwards nor downwards. This can be proved taking the values of the points on such a line and substituting them in the above equation of slope.
- The slope of a vertical line or a line which is parallel to y – axis is undefined i.e. vertical line has no slope.
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