Question

Line L passes through the points (1,3) and (-3,4). 
a) Fine the slope of line L. 
b) Find the y-intercept of L. 
c) Find the x-intercept of L. 
d) Find b so that line L passes through the point (-4,b).

Answer 1

a)

Given points are (1,3) and (-3,4)

Let (x1, y1) = (1,3) and (x2, y2) = (-3,4)

Slope of a Line (m)  =  (y2 - y1) / (x2 - x1)

                                =  (4 - 3) / (-3 - 1 )

                                =  - 1 / 4

b)

Point Slope form of line equation  (y - y1)  =  m (x -x1)

Substitute (x1, y1) = (1,3) and m = -1/4 in above equation

(y - 3)  =  -1/4 (x - 1)

4(y - 3)  =  -1 (x - 1)

4y - 12  =  -x + 1

4y + x  =  1 + 12

x + 4y  =  13 ----------> (1)

To find y - intercept Substitute x = 0 in Eq (1)

0 + 4y  =  13

4y  =  13

 

y  =  13/4.

 

c)

 

To find x - intercept Substitute y = 0 in Eq (1)

 

x + 4(0)  =  13

 

x  =  13

 

d)

 

Substitute (x, y) = (-4, b) in Eq (1)

 

-4 + 4(b)  =  13 

 

4b  =  13 + 4

 

4b  =  17

 

b  =  17/4

 

Answer :

 

a) Slope of a Line is -1/4.

 

b)  Y - intercept is 13/4

 

c)  x - intercept is 13.

 

d) The Value of b is 17/4.