17) through: (1,1) parallel to y=(1)/(6)x-3 A) y=(5)/(6)x+(1)/(6) B) y=(1)/(6)x-(5)/(6) C) y=-(5)/(6)x+(1)/(6) D) y=(1)/(6)x+(5)/(6)

To find the equation of a line that passes through the point and is parallel to the line , we need to use the fact that parallel lines have the same slope.The slope of the given line is . Since the line we are looking for is parallel to this line, it will also have a slope of .Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by: where is a point on the line and is the slope.Substituting the given point and the slope into the point-slope form, we get: Simplifying this equation, we have: Adding 1 to both sides, we get: Therefore, the equation of the line that passes through the point and is parallel to is .So, the correct answer is D) .