Explanation:
To find the equation of the line L2, which is perpendicular to the line L with the equation y = 3x - 4, you'll need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
The slope of line L is 3 (from the coefficient of x in y = 3x - 4). To find the slope of L2, you take the negative reciprocal of 3, which is -1/3.
Now that you have the slope (-1/3) of L2 and a point it passes through (9, 5), you can use the point-slope form of a line to find the equation of L2:
y - y1 = m(x - x1)
where (x1, y1) is the point (9, 5) and m is the slope (-1/3).
y - 5 = (-1/3)(x - 9)
Now, distribute the (-1/3) on the right side:
y - 5 = (-1/3)x + 3
Next, isolate y by adding 5 to both sides:
y = (-1/3)x + 8
So, the equation of line L2 is:
y = (-1/3)x + 8