Final answer:
The point-slope form of a line is represented as y - y1 = m(x - x1), where 'm' denotes the slope and (x1, y1) is the point through which the line passes. To provide the correct form of the student's line, we need the slope's numerical value which is missing in the question.
Step-by-step explanation:
The subject of the student's question is figuring out the point-slope form of a line given a point (3,2) and a slope (m). The point-slope form of a linear equation is expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.
In the given problem, we're told the line passes through the point (3, 2) and has a slope (m). To plug these values into the point-slope form, we have:
y - 2 = m(x - 3)
However, the student's question seems to contain a typo in the slope value, representing it as 'm' without providing an actual numerical value. To accurately determine which provided option represents the correct point-slope form, we need a specific value for the slope. Following the structure provided by the point-slope equation, if we assume 'm' is a placeholder for the slope's numerical value, the correct equation would resemble the format we presented:
y - 2 = m(x - 3).
Comparing this to the options presented by the student, since there are typos and inconsistencies, I’ll need to clarify the slope's value before confirming the correct point-slope form equation. However, one of the given examples y = 9 + 3x shows how the b and m terms determine the shape of the line on the graph where b is the y-intercept and m is the slope.