Question

What is the equation of a line, in point-slope form, that passes through (−2,−6) and has a slope of 1/3?

a. y+2=1/3(x+6)
b. y−2=1/3(x−6)
c. y+6=1/3(x+2)
d. y−6=1/3(x−2)

Answer 1

The equation of the line in point-slope form is y + 6 = 1/3(x + 2). This formulation allows for a clear representation of the line's characteristics. So, the option c is correct

Step-by-step explanation:

The equation of a line in point-slope form can be determined using the formula y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m is the slope.

For a line passing through the point (-2, -6) with a slope of 1/3, substituting these values into the formula yields: y - (-6) = 1/3(x - (-2)).

Simplifying this expression results in y + 6 = 1/3(x + 2).

Consequently, the equation of the line in point-slope form is expressed as y + 6 = 1/3(x + 2).

This formulation allows for a clear representation of the line's characteristics, with the slope and a specific point defining its trajectory in a concise mathematical framework.

Hence, the option c is correct, the equation of the line in point-slope form is y + 6 = 1/3(x + 2).