Final answer:
To find the equation of line d parallel to line c with a given point, use the slope from line c (-7/6) and the point-slope form with the point (5, -7). The resulting equation is y + 7 = -7/6(x - 5).
Step-by-step explanation:
The equation of line c is given as y – 6 = -7/6(x – 5). To find the equation of line d which is parallel to line c and passes through the point (5, –7), we need to use the same slope because parallel lines have equal slopes.
The slope of line c is -7/6, and we can use the point-slope form of a line to find the equation of line d.
Point-slope form is given by y – y1 = m(x – x1), where m is the slope and (x1, y1) is a point on the line. Since line d passes through (5, –7), and has a slope of -7/6, its equation can be written as:
y – ( –7) = -7/6(x – 5)
Simplifying the equation, we get:
y + 7 = -7/6(x – 5)
This is the equation of line d.