For which b the graph of the function y = 2x + b passes through one point of the segment AD, where A (1; 1). D (1; -1).

We have the function y = 2 * x + b. Let us find the values of b at which the graph of the function passes through one point of the segment AD, where A (1; 1), D (1; -1).

The main thing is not to confuse a straight line with a segment. The difference is that the segment has ends, and we know the coordinates of the ends.

Find the values of b at which the line passes through the ends of the segment, and then find those values of b.

We substitute the values of the ends of the segment into the straight line formula:

1 = 2 * 1 + b; b = -1.

-1 = 2 * 1 + b; b = -3.

It turns out that the line will intersect the segment AD for values of b from the interval [-3; -one].