Question

Which system is represented by the graph?

A. y=3x-2 y=3x-1
B. y=-3x-2 y=-3x-1
C.y=1/3x-2 y=1/3x-1
D.y=3x+2 y=3x+1

Answer 1

Answer: A. y=3x-2 y=3x-1

Explanation:

FRom the given graph, it can be seen that

Blue line passes through (1,2) and (0,-1)

Red line passes through (1,1) and (2,4)

As we know , equation of line passes through points (a,b) and (c,d) :

`(y-b)=(d-b)/(c-a)(x-a)`

Then , Equation of blue line will be :

`(y-(-1))=(2-(-1))/(1-0)(x-0)\\\\\Rightarrow\ y+1=3x\\\\\Rightarrow\ y=3x-1` ...(i)

Then , Equation of red line will be :

`(y-1)=(4-1)/(2-1)(x-1)\\\\\Rightarrow\ y-1=3(x-1)\\\\\Rightarrow\ y-1=3x-3\\\\\Rightarrow\ y=3x-2`....(ii)

From (i) and (ii) , the required equations are :

`y=3x-2;\ y=3x-1`

Hence, the correct option is A. y=3x-2 y=3x-1.