Question

The equation of a line is 2x + 3y = Select three lines that are parallel to the given line.

Answer 1

Answer:

The three lines that are parallel to the Given line are :

2x + 3y = 2

9y = -6x + 15

3y = -2x + 12

Step-by-step explanation:

The exact question is as follows :

Given - The equation of a line is 2x + 3y = 4.

To find - Select three lines that are parallel to the given line.

A) 2x + 3y = 2

B) 2x + 5y = 15

C) 9y = -6x + 15

D) 3y = -2x + 12

E) 3x - 2y = 15

Solution -

We know that,

If the slopes are the same and the y-intercepts are different, the lines are parallel.

Given that,

The given line is 2x + 3y = 4

⇒3y = -2x + 4

⇒y = -(2/3)x + (4/3)

So,

Slope = -(2/3)

y-intercept = (4/3)

Now,

A.)

2x + 3y = 2

⇒3y =  - 2x + 2

⇒y = -(2/3) + (2/3)

So,

Slope = -(2/3)

y-intercept = (2/3)

By Comparing with the given line's slope and y-intercept

We can see that

slope is same but y-intercept is different

So,

2x + 3y = 2 is parallel to the given line.

Now,

B.)

2x + 5y = 15

⇒5y =  - 2x + 15

⇒y = -(2/5) + (15/5)

So,

Slope = -(2/5)

y-intercept = 3

By Comparing with the given line's slope and y-intercept

We can see that slope is different

So,

2x + 5y = 15 is not parallel to the given line.

C)

9y = -6x + 15

⇒y = -(6/9)x + (15/9)

     = -(2/3)x + (5/3)

⇒y =  -(2/3)x + (5/3)

So,

Slope = -(2/3)

y-intercept = 5/3

By Comparing with the given line's slope and y-intercept

We can see that slope is same and y-intercept is different

So,

9y = -6x + 15 is parallel to the given line.

D)

3y = -2x + 12

⇒y = -(2/3) + (12/3)

So,

Slope = -(2/3)

y-intercept = 4

By Comparing with the given line's slope and y-intercept

We can see that slope is same and y-intercept is different

So,

3y = -2x + 12 is parallel to the given line.

E)

3x - 2y = 15

⇒-2y = -3x + 15

⇒2y = 3x - 15

⇒y = (3/2) - (15/2)

So,

Slope = 3/2

y-intercept = -15/2

By Comparing with the given line's slope and y-intercept

We can see that slope is different

So,

3x - 2y = 15 is not parallel to the given line.

∴ we get

The three lines that are parallel to the given line are :

2x + 3y = 2

9y = -6x + 15

3y = -2x + 12