Maths-

General

Easy

Question

# Identify the parallel lines and perpendicular lines from the given set. Application

2x + y = 1

9x + 3y = 6

y = 3x

y = -3x

2y = 4x +6

Y = - x/2

Hint:

### 1. Standard form of equation of a straight line is y = mx + c.

2. Slopes of parallel lines are equal.

3. Slopes of perpendicular lines are negative reciprocals of each other.

## 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 + 1

Comparing 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 + 0

Comparing 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 + 0

Comparing 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)

### Related Questions to study

Maths-

### A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.

### A line l touches the Y-axis at point 3 and has slope –3. Find the slope of the line perpendicular to the line l.

Maths-General

Maths-

### Identify the equation of a line parallel to the line y = x – 1

### Identify the equation of a line parallel to the line y = x – 1

Maths-General

Maths-

### The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?

### The sum of the radius and height of a cylinder is 21 cm and the T.S.A of the cylinder is 660 sq. cm. Find the height and volume of the cylinder?

Maths-General

Maths-

### Identify the equation of a line perpendicular to the line x/2 + y = -1

### Identify the equation of a line perpendicular to the line x/2 + y = -1

Maths-General

Maths-

### A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application

### A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis? Application

Maths-General

Maths-

### Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

### Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

Maths-General

Maths-

### Find the equation of line such that its y-intercept is 20 and slope is ½.Application

### Find the equation of line such that its y-intercept is 20 and slope is ½.Application

Maths-General

Maths-

### Identify the line having y-intercept = 1/2

### Identify the line having y-intercept = 1/2

Maths-General

Maths-

### Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x. Application

### Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x. Application

Maths-General

Maths-

### Two solid cylinders with radii 5 cm and 10 cm and lengths of 7 cm and 5 cm respectively are melted and recast into a cylindrical disc of thickness 3 cm, Calculate its radius.

### Two solid cylinders with radii 5 cm and 10 cm and lengths of 7 cm and 5 cm respectively are melted and recast into a cylindrical disc of thickness 3 cm, Calculate its radius.

Maths-General

Maths-

### Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.Application

### Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.Application

Maths-General

Maths-

### A Cylinder tank has a 75 cm diameter and 1.8 m height. Find the capacity in litres to three significant figures?

### A Cylinder tank has a 75 cm diameter and 1.8 m height. Find the capacity in litres to three significant figures?

Maths-General

Maths-

### The graph shows the subscription cost to a certain club in town. Write an equation of the Application

line. Explain what the slope and y-intercept mean in this situation. Then find the total

cost for 2 years.

### The graph shows the subscription cost to a certain club in town. Write an equation of the Application

line. Explain what the slope and y-intercept mean in this situation. Then find the total

cost for 2 years.

Maths-General

Maths-

### Identify the line having slope 2.

### Identify the line having slope 2.

Maths-General

Maths-

### A Rectangular piece of cardboard with dimensions 6 inches by 8 inches is used to make the curved side of a cylinder-shaped container. Using this cardboard What is the greatest volume of the cylinder can hold?

### A Rectangular piece of cardboard with dimensions 6 inches by 8 inches is used to make the curved side of a cylinder-shaped container. Using this cardboard What is the greatest volume of the cylinder can hold?

Maths-General