Alright, let's tackle this problem. Remember that the standard form for the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. In this case, we've been given that the slope, m, is 6.
We also need to figure out the y-intercept. Since we know a point on the line is (8, 7), we can use these values in the equation of the line. Because we know that the x-coordinate, or the horizontal position, of this point is 8, and the y-coordinate, or the vertical position, is 7. So we can substitute these values, along with the slope, into the formula and solve for b, the y-intercept. When you calculate it, you'll have the equation y = 6x +b.
Now to answer the question, let's see which equation matches ours. We have the following options:
A) y = 6x + 7
B) y = 7x + 8
C) y = 8x + 6
D) y = 6x - 7
The correct answer is y = 6x - 7, which matches with our calculated equation. Therefore, the correct answer is option D)}. This is the equation of the line with slope 6 and containing the point (8, 7).