Mathematics
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
Putting x and y = 0 in y = 2x we get,
Both sides = 0.
So, line y = 2x passes through origin.
A → L3.
Putting x = 0 in y - 2x + 2 = 0,
⇒ y - 2(0) + 2 = 0
⇒ y = -2.
Putting y = 0 in y - 2x + 2 = 0
⇒ 0 - 2x + 2 = 0
⇒ 2x = 2
⇒ x = 1.
So, x-intercept is positive and y-intercept is negative.
B → L4.
Putting x = 0 in 3x + 2y = 6,
⇒ 3(0) + 2y = 6
⇒ 2y = 6
⇒ y = 3.
Putting y = 0 in 3x + 2y = 6
⇒ 3x + 2(0) = 6
⇒ 3x = 6
⇒ x = 2.
So, both intercept are positive.
C → L2.
Comparing y = 2 with y = mx + c we get,
Slope (m) = 0.
So, the line y = 2 is parallel to x-axis.
D → L1.
Hence, A → L3, B → L4, C → L2 and D → L1.
Related Questions
The point P is the foot of perpendicular from A(-5, 7) to the line 2x - 3y + 18 = 0. Determine :
(i) the equation of the line AP
(ii) the co-ordinates of P
Th points A, B and C are (4, 0), (2, 2) and (0, 6) respectively. Find the equations of AB and BC.
If AB cuts the y-axis at P and BC cuts the x-axis at Q, find the coordinates of P and Q.
The line 5x - ky + 3 = 0 passes through the point (x = y = 3). The value of k is :
-3
-6
6
3