Maths-

General

Easy

Question

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

- y = 2x + 1
- x = 2y +2
- 4y – 8x = 2
- x = 2y

Hint:

### Y-intercept for a line is a point at which the given line intersects with the y-axis i.e. the point at which x = 0.

## The correct answer is: 4y – 8x = 2

### Step-by-step solution:-

The given line has y-intercept = 1/2.

y-intercept is the point at which x-coordinate is 0

∴ The given point is (0,1/2)

We substitute (0,1/2) in the given equations to find whether LHS = RHS or not.

a. y = 2x + 1

∴ 1/2 = 2 (0) + 1

∴ 1/2 = 0 + 1

∴ 1/2 ≠ 1

∴ LHS ≠ RHS

b. x = 2y +2

∴ 0 = 2 (1/2) + 2

∴ 0 = 1 + 2

∴ 0 ≠ 3

∴ LHS ≠ RHS

c. 4y – 8x = 2

∴ 4 (1/2) - 8 (0) = 2

∴ 2 - 0 = 2

∴ 2 = 2

∴ LHS = RHS

d. x = 2y

∴ 0 = 2 (1/2)

∴ 0 ≠ 1

∴ LHS ≠ RHS

Final Answer:-

∴ Option c i.e. 4y - 8x = 2 is the correct option.

Note:-

Alternatively, we can simplify the given equations and compare it with slope-intercept formula to find the value of y-intercepts-

a. y = 2x + 1

∴ Comparing this equation with y = mx + b, we get b = 1 ≠ 1/2

b. x = 2y +2

∴ x - 2 = 2y

∴ (x - 2) / 2 = y

∴ 1/2 x - 2/2 = y

∴ 1/2 x - 1 = y

i.e. y = 1/2 x - 1

Comparing this equation with y = mx + b, we get b = -1 ≠ 1/2

c. 4y – 8x = 2

∴ 2y - 4x = 1 .................. (Dividing both sides by 2)

∴ 2y = 4x + 1

∴ y = 2x + 1/2 ...... (Dividing both sides by 2)

∴ Comparing this equation with y = mx + b, we get b = 1/2

d. x = 2y

∴ 1/2 x = y ................. (Dividing both sides by 2)

i.e. y = 1/2 x + 0

Comparing this equation with y = mx + b, we get b = 0 ≠ 1/2

∴ Option c i.e. 4y - 8x = 2 has y-intercept = 1/2

### Related Questions to study

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

Maths-

### A certain population of bacteria had an initial population of 1500. It then started growing at a rate of 2000 per day. Write the Application equation to model this situation. What are the slope and y-intercept? Explain.

### A certain population of bacteria had an initial population of 1500. It then started growing at a rate of 2000 per day. Write the Application equation to model this situation. What are the slope and y-intercept? Explain.

Maths-General

Maths-

### Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).

### Find equation of a line parallel to line with an equation y = 5x + 1 and passing through (1, 10).

Maths-General

Maths-

### A mango candy costs $5 and a strawberry candy costs $3. Alex wants to buy both types of candies and he has $40 with him .Application Write an equation in standard form Ax + By = C that models this situation. What do the values of A, B, and C mean in this situation?

### A mango candy costs $5 and a strawberry candy costs $3. Alex wants to buy both types of candies and he has $40 with him .Application Write an equation in standard form Ax + By = C that models this situation. What do the values of A, B, and C mean in this situation?

Maths-General

Maths-

### If the equation of a line is 2x – 3y = 6, find its slope and y-intercept.

### If the equation of a line is 2x – 3y = 6, find its slope and y-intercept.

Maths-General

Maths-

### You can rent books at a local store for $5.00 each. An Internet company offers a flat fee of $20.00 per month for as many books as you want. How many books do you need to rent to make the online rental a better buy?

### You can rent books at a local store for $5.00 each. An Internet company offers a flat fee of $20.00 per month for as many books as you want. How many books do you need to rent to make the online rental a better buy?

Maths-General

Maths-

### An insulated collar is made to cover a pipe. Find the volume of the material used to make the collar. Let r=3 inches, R=5 inches and h= 21 inches.

### An insulated collar is made to cover a pipe. Find the volume of the material used to make the collar. Let r=3 inches, R=5 inches and h= 21 inches.

Maths-General

Maths-

### Find the slope and write the equation of the given line.

### Find the slope and write the equation of the given line.

Maths-General

Maths-

### Find the value of p so that

### Find the value of p so that

Maths-General