## FIND THE SLOPE OF THE LINE CONTAINING THE GIVEN POINTS

Find Slope of the Line Containing the Given Points :

Here we are going to see, how to find the slope of the line using the given points.

Slope :

If (x1,y1) and (x2,y2) are any two points on a line, with x1x2, then the slope of the line is

(y2 − y1) / (x2 − x1)

## Find Slope of the Line Containing the Given Points - Examples

Question 1 :

Find the slope of the line that contains the points (3, 4) and (7, 13).

Solution :

Slope m  =  (y2 - y1)/ (x2 - x1)

(x1, y1)  ==>  (3, 4) and (x2, y2)  ==>  (7, 13)

m  =  (14 - 4)/(7 - 3)

m  =  10/4

m  =  5/2

Question 2 :

Find the slope of the line that contains the points (2, 11) and (6,−5).

Solution :

Slope m  =  (y2 - y1)/ (x2 - x1)

(x1, y1)  ==>  (2, 11) and (x2, y2)  ==>  (6, -5)

m  =  (-5 - 11)/(6 - 2)

m  =  -16/4

m  =  -4

Question 3 :

Find a number t such that the line containing the points (1, t) and (3, 7) has slope 5.

Solution :

Slope m  =  (y2 - y1)/ (x2 - x1)

(x1, y1)  ==>  (1, t) and (x2, y2)  ==>  (3, 7)

m  =  5

5  =  (7 - t)/(3 - 1)

5  =  (7 - t)/2

10  =  7 - t

t  =  7 - 10

t  =  -3

Question 4 :

Find a number c such that the line containing the points (c, 4) and (−2, 9) has slope −3.

Solution :

Slope m  =  (y2 - y1)/ (x2 - x1)

(x1, y1)  ==>  (c, 4) and (x2, y2)  ==>  (-2, 9)

m  =  -3

-3  =  (9-4)/(-2-c)

-3  =  -5/(2 + c)

3(2 + c)  =  5

6 + 3c  =  5

3c  =  -1

c  =  -1/3

Question 5 :

Find a number t such that the point (3, t) is on the line containing the points (7, 6) and (14, 10).

Solution :

From the given question, we know that all the three points lie on the same line.

Slope of line with the points (3, t) and (7, 6) will be equal to the slope of the line with the points (7, 6) and (14, 10).

Slope m  =  (y2 - y1)/ (x2 - x1)

 (3, t) and (7, 6)m  =  (6 - t)/(7 - 3)m  =  (6 - t)/4 -----(1) (7, 6) and (14, 10)m  =  (10 - 6)/(14 - 7)m  =  4/7 -----(2)

(6 - t)/4  =  4/7

7(6 - t)  = 16

42 - 7t  =  16

42 - 16  =  7t

7t  =  26

t  =  26/7

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