SLOPE OF A LINE

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Learning Contents:

·         Meaning of Slope

·         Types of Slope

·         Calculating slope numerically

Slope

Slope measures the steepness and tells the direction of a line. It indicates the rate of change i.e. how fast y is changing with respect to x. In other words, slope is the difference between the two points in the vertical direction (rise) and then divide by the difference in the horizontal direction (run). The formula of the slope is rise over run. 


Whereas,

Rise indicates the movement (up or down) of a point along the y- axis i.e. Δ Y=Y2-Y1      

 Run indicates the movement (left or right) of point long the x-axis i.e. Δ X=X2-X1

 

Types of Slope

The slope of a line is classified into four different categories that are as follows:

1.      Positive Slope

2.      Negative slope

3.      Zero Slope

4.      Undefined Slope

 

1.      Positive slope is a slope when the line goes uphill from left to right. It has an increasing slope. It is like climbing up a hill. It is called a positive slope as the line is rising up. The value of the slope would be positive. A positive slope is further classified into two types: a. Steep upward slope ( High slope)  b. Shallow upward slope ( Low slope)

The figures a. Steep upward slope and b. Shallow upward slope are shown below:


2.      Negative slope is a slope when the line goes downhill from left to right. It has a decreasing slope. It is like climbing down a hill.  It is called a negative slope as the line is falling down. The value of the slope would be negative. A negative slope is further classified into two types: a. Steep downward ( High negative slope)  b. Shallow downward ( Low negative slope)

The figures a. Steep downward slope and b. Shallow downward slope are shown below:



3.      Flat (zero slope) is a slope when the line is horizontal i.e. parallel to X-axis. The slope of the horizontal line is always zero.

The figure a. zero slope is given below: 

 

4.      Vertical Slope ( undefined slope) is a slope when the line is vertical i.e. parallel to Y-axis. It is also called infinite slope. The slope of a vertical line is undefined.

The figure b. vertical slope is given below:

Calculating slope numerically:

Graphically, it is quite unfair to find out which curve is steeper. Hence, the best way is to calculate the steepness of a curve is numerically It is very important to know that slope of a line is calculated between any two points on the curve. The slope of a linear function will remain the same no matter where on the line it is measured. In other words, all the points on a straight line will have an equal slope.  An important thing to understand here is while calculating the slope of a curve, if the answer turns out to be negative i.e. slope of the curve has a  downward slope or vice versa.

To find the slope of a curve, we will have to find the following things:

a. Rise (Vertical distance on Y-axis or change in Y) i.e. how much does it go up or down?

b. Run (Horizontal distance on X-axis or change in X) i.e. how much does it go side to side?

 



Practice Questions

 It’s your turn now!

1. What is the slope of a line passing through points (-1, 2) and (-4, -4)?

a. 1

b. 2

c. 3

d. -2

2. What is the slope of a line passing through points (-9, 6) and (18, -18)?

a. -8/9

b. 9/8

c. -9/8

d. 8/9

3.  Find the value of y1 when  x1 = - 4, x2 = - 8, y2 = 7 and slope is -7/4.

a. 0

b. -7

c. 7

d. 8

Answer Key

1.b

2.a

3.a

 


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