Chapter 13.2, Problem 22PSC

To determine

To find: The equations of two possible lines.

Answer to Problem 22PSC

The equations of two possible lines are $y=\sqrt{3}x+2$ and $y=-\sqrt{3}x+2$ .

Explanation of Solution

Given:

The $y$ intercept is 2 and angle from x-axis is $60°$ .

Calculation:

There are two possibilities of slope.

  $\begin{array}{c}{m}_1=\tan 60°\\ =\sqrt{3}\\ m_2=\tan 120°\\ =-\sqrt{3}\end{array}$

Substitute $\sqrt{3}$ for $m_1$ , and 2 for $b$ in the equation $y=m{1}_{}x+b$ .

  $y=\sqrt{3}x+2$

Substitute $-\sqrt{3}$ for $m_1$ , and 2 for $b$ in the equation $y=m{1}_{}x+b$ .

  $y=-\sqrt{3}x+2$

Therefore, the equations of two possible lines are $y=\sqrt{3}x+2$ and $y=-\sqrt{3}x+2$ .