Final answer:
The equation of a line with a slope of 1/3 that passes through the point (-2, 1) is found using the point-slope form and simplifying to get y = 1/3x + 5/3, which is option B.
Step-by-step explanation:
The question asks for the equation of a line that has a slope (m) of 1/3 and passes through the point (-2, 1). To find the equation of this line, we'll use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting our given point (-2, 1) and slope 1/3 into the point-slope form gives us:
y - 1 = 1/3(x + 2)
Simplifying this equation yields:
y - 1 = 1/3x + 1/3(2)
Add 1 to both sides of the equation to isolate y:
y = 1/3x + 2/3 + 1
Combining like terms (2/3 and 1) gives us the final equation:
y = 1/3x + 5/3
Therefore, the correct equation that represents the line is B) y = 1/3x + 5/3, as it satisfies the slope and the point given.