Maths-
General
Easy

Question

# Identify the parallel lines and perpendicular lines from the given set. Application2x + y = 19x + 3y = 6y = 3xy = -3x2y = 4x +6Y = - x/2 Hint:

## The correct answer is: ∴ line e (2y = 4x +6) and line f (Y = - x/2) are perpendicular lines & line b (9x + 3y = 6) and line d (y = -3x) are parallel lines.

### Step-by-step solution:-We will simplify the given equations and compare the same with standard form of a straight line to find the value of m.a. 2x + y = 1∴ y = -2x + 1Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = -2 ......................... (Equation i)b. 9x + 3y = 6∴ 3y = -9x + 6∴ y = -3x + 2 ............................ (Dividing both sides by 3)Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = -3 ......................... (Equation ii)c. y = 3x∴ y = 3x + 0Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = 3 ......................... (Equation iii)We know that slopes of perpendicular lines are negative reciprocals of each other.and we observe that- Slope of line e (2y = 4x + 6) = 2 ...................................................... (From Equation v)∴ Slope of line e (2y = 4x + 6) = -1/ -1/2 …........................................ (Multiplying and dividing by -1/2)∴ Slope of line e (2y = 4x + 6) = -1/ Slope of line f (y = -x/2) ........... (From Equation vi)∴ Slope of line e and f are negative reciprocals of each other∴ line e (2y = 4x +6) and line f (Y = - x/2) are perpendicular lines.Also, We know that slopes of parallel lines are equal.and we observe that-Slope of line b (9x + 3y = 6) = Slope of line d (y = -3x) = -3 .............. (From Equation ii & iv)∴ line b (9x + 3y = 6) and line d (y = -3x) are parallel lines.d. y = -3x∴ y = -3x + 0Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = -3 ......................... (Equation iv)e. 2y = 4x +6∴ y = 2x + 3 .................................... (Dividing both sides by 2)Comparing the above equation with standard form of a line i.e. y = mx + c, we get- m = 2 ......................... (Equation v)  #### With Turito Foundation. #### Get an Expert Advice From Turito.  