Final answer:
To find the equation of a line given a point (3,2) and a slope of -2/3, the point-slope formula is used, resulting in the final equation of the line as y = -(2/3)x + 4.
Step-by-step explanation:
The student is asking how to find the equation of a line given a point on the line and its slope. Given a point P=(3,2) and a slope m=-2/3, the equation of the line can be found using the point-slope form of a line: y - y1 = m(x - x1).
Plugging the supplied values into the point-slope form yields the equation:
y - 2 = -(2/3)(x - 3)
Which simplifies to:
y = -(2/3)x + 2 + 2
Therefore, the equation of the line is y = -(2/3)x + 4.