Question

1. find the equation of the line with a slope angle of 60° that goes through the point (0,9). assume the line has a positive slope.

Explanation:

Step1: Find the slope

The slope \(m\) of a line with slope angle \(\theta\) is \(m = \tan\theta\). Given \(\theta = 60^{\circ}\), then \(m=\tan60^{\circ}=\sqrt{3}\).

Step2: Use the slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
The line passes through the point \((0,9)\). Substituting \(x = 0\) and \(y = 9\) into \(y=mx + b\), we get \(9=m\times0 + b\), so \(b = 9\).
Since \(m=\sqrt{3}\) and \(b = 9\), the equation of the line is \(y=\sqrt{3}x + 9\).

Answer:

\(y=\sqrt{3}x + 9\)