Final answer:
The given line equation is rewritten into slope-intercept form as y = (1/6)x + 2. The slope of the line is 1/6. The equation of a parallel line passing through (6, 10) starts with y - 10 = (1/6)(x - 6) before simplifying.
Step-by-step explanation:
To rewrite the equation of the line -x + 6y = 12 into slope-intercept form (y = mx + b), we first need to isolate y on one side. Adding x to both sides gives us 6y = x + 12. Then, we divide each term by 6 to solve for y: y = (1/6)x + 2. This is the slope-intercept form of the equation, where m is the slope and b is the y-intercept.
The slope of the line is the coefficient of x in the slope-intercept form, which is 1/6 in our case.
To write the equation of a line parallel to the given line passing through the point (6, 10), we use the same slope of 1/6 since parallel lines have equal slopes. Using the point-slope form y - y1 = m(x - x1), we plug in the point (6, 10) and the slope 1/6 to get: y - 10 = (1/6)(x - 6). Simplifying this will give the equation in slope-intercept form.