Question

Which graph represents the inequality y<−1+2x?

Answer 1

The inequality is y<2x-1.

To draw the solutions, we first start our solution by drawing the line y=2x-1.

To draw a line, it is enough to determine 2 solutions (x, y), plot them in the coordinate axes, and finally join them by a line.

Let x=0, then y=2*0-1=0-1=-1, so we have the point (0, -1).

Now, if y=0, x=1/2, so we have the point (1/2, 0).

We can see that these 2 points are points of the lines on the 2 pictures on the left. Now we want to determine which region to color, the region below the line, or the one above it.

Consider any point which is not on the line, for example (1, 2). We plug x=1 and y=2 in the inequality. If the inequality holds, it means that we are in the solutions region. If it does not hold, then we are on the not solutions regions.

We check: for x=1, y=2 the inequality y<2x-1 is 2<1, which is not true. So the point (1, 2) can't be in the colored region.

Thus the answer is bottom left.

Answer: Bottom left picture.