Question

Question: Given the line y = 3/4x + 6 and a line L parallel to the given line and 4 units from it. A
possible equation for L is:


1. y = 3/4 x +1
2. y=3/4X
3. y = 3/4 x-1
4. y= 3/4 x-2
​

Answer 1

Answer:

Given the line y = 3/4x + 6 and a line L parallel to the given line and 4 units from it. A possible equation for L is: 1. y = 3/4 x +1.

Answer 2

Concept:

Steps to obtain distance between two parallel lines

Verify that the given parallel lines' equations are in the slope-intercept form (y=mx+c).

It is necessary to find the intercepts (c1 and c2) and slope value that are shared by the two lines.

Get the aforementioned values, and then use the slope-intercept equation to calculate y.

Finally, use the distance formula to calculate the distance between two parallel lines using all the previous information.

The form that the two parallel lines can take is

y = mx + c1 … (i)

also, y = mx + c2 (ii)

d=|c₁-c₂|/√(1+m²)

Given:

Given the line y = 3/4x + 6 and a line L parallel to the given line and 4 units from it.

Find:

find a possible equation for L

Solution:

d=|c₁-c₂|/√(1+m²)--------i

y=3/4x+6

c₁=6

m=3/4

d=4

Putting this value in eq 1

⇒4 = |6-c|/√(1+(3/4)²)

⇒4 = |6-c|/√25/16

⇒4 = |6-c|/(5/4)

⇒5= |6-c|

⇒±5=6-c

Either,

6-c=5

⇒c=1

or

6-c=-5

⇒c=11

So, possible equations are

y=3/4x+11 and

y=3/4x+1, option A is the answer

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