Answer:
y = (-3/2)x + 4.
Explanation:
y - 4 = (2/3)(x - 9)
y = (2/3)x - (2/3)(9) + 4
y = (2/3)x - 2
The slope of this line is 2/3.
A line that is perpendicular to this line will have a slope that is the negative reciprocal of 2/3. To find the negative reciprocal, we flip the fraction and change the sign:
slope of perpendicular line = -3/2
Now we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Substituting the given point (6,-5) and the slope -3/2, we get:
y - (-5) = (-3/2)(x - 6)
y + 5 = (-3/2)x + 9
y = (-3/2)x + 4
Therefore, the equation of the line that is perpendicular to y - 4 = (2/3)(x - 9) and passes through the point (6,-5) is y = (-3/2)x + 4.