Final answer:
The equation of the line passing through point p (-1,3) and making a 120-degree angle with the positive x-axis is y = √3x + 3 + √3, by first finding the complementary angle for the slope and then using the point-slope form.
Step-by-step explanation:
To find the equation of the line that passes through the point p (-1,3) and makes an angle θ = 120 degrees with the positive x-axis, we need to use trigonometry and the concept of slope.
Recall that the slope (m) of a line is the tangent of the angle it makes with the positive x-axis.
However, in this case, we are given the angle with respect to the positive x-axis, so we need to find the complementary angle to the x-axis, which is 180° - 120° = 60° for the slope calculation.
The slope (m) of the line is thus tan(60°), which is √3.
Using the point-slope form of a line's equation, y - y1 = m(x - x1), and plugging in the point (-1,3) and the slope √3, we get the equation y - 3 = √3(x + 1).
Simplifying, we get the final equation of the line: y = √3x + 3 + √3.