Given correct options to this question is:

A.  y = x -3

B. y = 3x - 3√2

C. y = x - 3√2

D. y = 3x - 3 Relevance

First, the picture is wrong. If the equation of the upper line is 3x, it should be much steeper. So all bets are off on any of the answers being correct.

We can agree that the slope of the two lines must be the same, so we can eliminate A and C which have the wrong slopes. We can also eliminate D because we know the lines aren't horizontal. Only if they were horizontal would the distance between the lines be the same as the distance between the origin and the y-intercept (circled in red on the y-axis.)

So it would seem that answer B makes the most sense. However, it turns out that isn't the right answer either.

Take two parallel lines:

y = mx + b₁

y = mx + b₂

The formula for the distance between two parallel lines is:

d = | b₁ - b₂ | / √(m² + 1)

In our case, our first line is through the origin so b₁ = 0. And our second line will be below that so b₂ is negative. The slope (m) for both is 3. The distance (d) is 3.

y = 3x

y = 3x + b₂

Plug in the values and we get:

3 = |0 - b₂| / √(3² + 1)

3 = |-b₂| / √10

3√10 = |-b₂|

We want a negative value for b₂ (because it is below the origin), so:

b₂ = -3√10

So actually none of the provided answers is correct.

y = 3x - 3√10

See the graph in the first link below.

• We saw this once before, right? The sketch appears to indicate that 3 is the distance between lines p and q, but that is not actually given in the question.

Taking only the conditions stated in the question, options (B) and (D) are both correct. If the lines must also be 3 units apart, then none of the available choices are correct.

• 3 is the distance between the lines. But - 3 is NOT the y-intercept. The y-intercept is < 3, so B would be a possible equation for the line.

You need to take the angle into account. If the lines were at a 45 degree angle to the x-axis, then the y-intercept would be -3√2.

Edit.

Yes, the question is messed up. B can't be right because the slope would have to be 1, not 3, for -3√2 to be the y-intercept.