Final answer:
The equation of a line passing through the origin and forming a 30° angle with the x-axis is derived using the tangent of the angle for the slope, leading to y = (⅔)x.
Step-by-step explanation:
To find the equation of a line that passes through the origin and makes a 30° angle with the x-axis, we can follow these steps:
- Identify the slope of the line. Since the line makes a 30° angle with the x-axis, the slope (m) is the tangent of that angle, which is tan(30°). The value of tan(30°) is ⅔ or approximately 0.577.
- Since the line passes through the origin, its y-intercept (b) is 0.
- Using the slope-intercept form of a line, which is y = mx + b, we can substitute our known values to get the equation. Therefore, the equation of this line is y = ⅔x.