Problem Solving

Lines $$y=\sqrt{3}x-2\ and\ y=\sqrt{3}x-5$$ intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

The OA is C.

Do I need to make the graph of the lines or I can use only the equations?

Vincen wrote:Lines $$y=\sqrt{3}x-2\ and\ y=\sqrt{3}x-5$$ intersect at what height above the x axis?

A. 0
B. 1/(√3)
C. 1
D. √3
E. 5

The OA is C.

Do I need to make the graph of the lines or I can use only the equations?

Hi Vincen,
Let's take a look at your question. It seems that you have typed the question incorrectly. I assume that the question you typed in the subject line is correct.

$$y=\sqrt{3}x-2 --- (i)$$ and
$$\ y=2\sqrt{3}x-5---(ii)$$
From Equation (i) we can write,
$$\sqrt{3}x=y+2 --- (iii)$$
From Equation (ii), we can write
$$\sqrt{3}x=\frac{y+5}{2} --- (iv)$$

Comparing Eq(iii) and (iv), to find height above the x axis, where the given lines intersect each other, i.e. y,
$$ y + 2 = \frac{y+5}{2}$$
$$\ 2(y+2) = y+5$$
$$\ 2y + 4 = y + 5 $$
$$\ 2y - y = 5 - 4 $$
$$\ y = 1$$

It means that the lines intersect each other at height 1.
Therefore, Option D is correct.

Hope this helps.

I am available if you'd like any follow up.