Line intersecting? Graphing?

Question

5x+4y=12. The graph of the equation above in the xy-plane is a line, l. Line l intersects line m at point [2,1/2]. Which of the following could be an equation of line m?

 

A) 2x= y/2

B) 2y=3-x

C) 2x+4y=8

D) y=4-5/4y

Answer 1

Line l and line m intersect at point [2,1/2]

 

It means [2,1/2] is also on line m 

 

so substitute the value of (x,y)=[2,1/2] in each equation and check which equation is true for [2,1/2]

 

 

A)2x=y/2

  2(2) = 1/2 /2

  4 = 1/4           not true

 

B)2y=3-x

  2(1/2) = 3-2

    1=1           true

 

C)2x+4y=8

2(2)+4(1/2)=8

4+2 =8

6=8               not true

 

D)y=4- 5/4x

1/2=4 - 5/4(2)

1/2 =4-5/2

1/2 =3/2     not true

 

Only 2y=3-x is the equation of line m