Question

Need help asap before I die these are my last words..

Which system of inequalities is represented by the graph?

a y < 2x
y ≤ 1

by > 2x
y ≥ 1

c y ≤ 2x
y < 1

d y ≥ 2x
y > 1

Answer 1

First you have to figure out what each equation is. The straight horizontal line is dotted so it is < or >. It runs through y = 1 and the shading is above it so our inequality for that one is y > 1. The other line is on a slant so it has a slope and since it is solid, it will be
`\leq` or
`\geq`. The line goes through the origin, so the y-intercept is 0, and from that point, if we go up 2 and over 1 we find another point on the line. That means that the slope is 2/1 or 2. Since it goes through the origin, the equation for that line is y = 2x. But we need the inequality. It looks like the solutions to this line are those that are above it, as well. So
`y \geq 2x`. Our solution, then, is the last choice above, d.