need help with my math assignment

Question

the line ax+by=c, where a>0,c>0, and b<0, is shifted three units down and two units right. What must be true about the slope of the translated function?

Answer 1

Solving for y, we get y = -(a/b)x + (c/b). So, the line has slope -a/b.

To shift the graph 2 units to the right, replace x by x-2. So, y = -(a/b)(x-2) + (c/b)

To shift the graph 3 units down, subtract 3 from y. So, y = -(a/b)(x-2) + (c/b) - 3.

Note that this line also has slope -a/b.

The slope of the translated graph is the same as the original graph.