Answer :
To determine the equation of a line with an inclination of 120° passing through the point (√3, -1), you can follow these steps:
1. The inclination of a line is the angle it makes with the positive direction of the x-axis. In this case, an inclination of 120° means the line slopes downward from left to right at a steep angle.
2. The slope of a line can be calculated using the tangent of the angle of inclination. The tangent of 120° is -√3. Therefore, the slope of the line is -√3.
3. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
4. Since the line passes through the point (√3, -1), you can substitute these coordinates into the equation to find the y-intercept, b. The equation becomes -1 = -√3(√3) + b.
5. Solving for b gives b = -1 + 3 + b, which simplifies to b = 2.
6. Now, you have the slope, m = -√3, and the y-intercept, b = 2. Plug these values into the slope-intercept form equation to get the final equation of the line: y = -√3x + 2.
Therefore, the equation of the line with an inclination of 120° passing through the point (√3, -1) is y = -√3x + 2.
