Write the equation of a line that goes through the point ( 6 ,6 ) and is parallel to the line y = 1 / 3x - 4.

Step 1: Identify the slope of the given line The equation of the given line is in the form y = mx + c, where m is the slope. Here, m = 1/3.

Step 2: Use the slope of the parallel line Parallel lines have the same slope. So, the slope of the line we want to find is also 1/3.

Step 3: Use the point-slope form of a line The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (6, 6) and has a slope of 1/3. Substituting these values in, we get:

y - 6 = 1/3(x - 6)

Step 4: Simplify the equation To simplify, distribute the 1/3 on the right side:

y - 6 = 1/3x - 2

Then, add 6 to both sides to solve for y:

y = 1/3x + 4

So, the equation of the line that goes through the point (6, 6) and is parallel to the line y = 1/3x - 4 is y = 1/3x + 4.