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Which equation represents a line that has a slope of ⅓ and passes through point (-2, 1)?

A) y = 1/3x - 1
B) y = 1/3x + 5/3
C) y = 1/3x - 5/3
D) y = 1/3x + 1

User Pintac
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1 Answer

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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.

User Ryan Ogle
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