Final answer:
To find the equation of the line parallel to x + 7y = 8 and passing through the point (6,8), we determined the slope of the given line (-1/7), and then used the point-slope form to arrive at the equation y = -1/7x + 50/7, which is the desired parallel line.
Step-by-step explanation:
The question asks us to write the equation of a line that passes through a given point (6,8) and is parallel to a given line whose equation is x + 7y = 8. To find the equation of a line parallel to this one, we must first identify the slope of the line. Rewriting the given equation in slope-intercept form, where y = mx + b, we get y = -1/7x + 8/7. The slope (m) of the line is -1/7. Since parallel lines have the same slope, our new line will also have a slope of -1/7.
Now, using the point-slope form y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we substitute (6,8) for (x1, y1) and -1/7 for m to get y - 8 = -1/7(x - 6). Simplifying this, we arrive at the equation of the line parallel to the given line and passing through the given point: y = -1/7x + 50/7.