Question

Which of the following equations represents a line that passes through the point (9, -1) and is parallel to the line y = (1/3)x + 11?

A) y = (1/3)x + 8
B) y = (1/3)x - 1
C) y = (1/3)x + 11
D) y = (1/3)x - 4

Answer 1

To find the equation of a line parallel to y = (1/3)x + 11 and passing through the point (9, -1), we can use the fact that parallel lines have the same slope. The equation of the line is y = (1/3)x - 4.

Step-by-step explanation:

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope. The given line has a slope of 1/3. So, the equation of the parallel line can be written as y = (1/3)x + b, where b is the y-intercept. To find the value of b, we can substitute the coordinates of the given point (9, -1) into the equation.

-1 = (1/3)(9) + b

-1 = 3 + b

b = -4

Therefore, the equation of the line that passes through the point (9, -1) and is parallel to the line y = (1/3)x + 11 is y = (1/3)x - 4. The correct answer is option D.