The equation of line L is (A-2) y = (3a-1) X-1. If line L does not pass through the second quadrant, what is the value range of a? A is greater than or equal to 2

The equation of line L is (A-2) y = (3a-1) X-1. If line L does not pass through the second quadrant, what is the value range of a? A is greater than or equal to 2

① When a = 2, the line L is: 5x = 1, it does not pass through the second quadrant, so a = 2 satisfies the condition
② When a ≠ 2, in order that the line L does not pass through the second quadrant, the slope k is greater than 0, and the intercept on the Y axis is less than 0
The slope of line L is: k = (3a-1) / (A-2) > 0, ①
The intercept on the y-axis is: - 1 / (A-2) < 0
From 2, A-2 ＞ 0, that is, a ＞ 2,
The inequality (1) is equivalent to 3a-1 ＞ 0, a ＞ 1 / 3
The value range of a satisfying the condition is a > 2
In conclusion, the value range of a satisfying the condition is: a ≥ 2

The sine value of the inclination angle of a straight line and y-axis is 4 / 5 compared with the point P (0,2),

If the sine value of the tilt angle is 4 / 5, the cosine value of the tilt angle may be - 3 / 5 or 3 / 5
Then the slope is - 4 / 3 or 4 / 3
Then the equation of the straight line is:
Y = (4 / 3) x + 2 or y = - (4 / 3) x + 2