Question

Match the equations A, B, C and D with the lines L₁, L₂, L₃ and L₄, whose graphs are roughly drawn in the given diagram.

A ≡ y = 2x; 

B ≡ y – 2x + 2 = 0;

C ≡ 3x + 2y = 6;

 D ≡ y = 2

Answer 1

Putting x = 0 and y = 0 in the equation y = 2x, we have:

LHS = 0 and RHS = 0

Thus, the line y = 2x passes through the origin.

Hence, A = L₃

Putting x = 0 in y − 2x + 2 = 0, we get, y = −2

Putting y = 0 in y − 2x + 2 = 0, we get, x = 1

So, x-intercept = 1 and y-intercept = −2

So, x-intercept is positive and y-intercept is negative.

Hence, B = L₄

Putting x = 0 in 3x + 2y = 6, we get, y = 3

Putting y = 0 in 3x + 2y = 6, we get, x = 2

So, both x-intercept and y-intercept are positive.

Hence, C = L₂

The slope of the line y = 2 is 0.

So, the line y = 2 is parallel to x-axis.

Hence, D = L₁