Final answer:
To find the equation of line d, which is parallel to line c and passes through the point (10, -9), we use the fact that parallel lines have the same slope. The equation of line d is y = -67x + 661.
Step-by-step explanation:
To find the equation of line d, which is parallel to line c and passes through the point (10, -9), we use the fact that parallel lines have the same slope. Since line c has the equation y = -67x - 1, its slope is -67. Therefore, the slope of line d is also -67.
We can now use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values for point (10, -9) and slope -67, we get y - (-9) = -67(x - 10).
Simplifying the equation gives us y + 9 = -67x + 670. To write it in slope-intercept form, we subtract 9 from both sides to get y = -67x + 661. Therefore, the equation of line d is y = -67x + 661.