Question

Which system is represented by the graph? Really need help!!!!!!!!!
Graph added!

Answer 1

A. y > - x + 2
y ≤ 2x - 1

B. y ≤ -x + 2
y < 2x - 1


C. y ≥ - x - 1
y < 2x + 2


D. y < - x - 1
y ≥ 2x + 2

Answer 2

It looks like no one has helped you yet, so I'll do that! The line that is going uphill has a positive slope. Do you know how to find equations of lines from looking at the graph? The slope-intercept method would be useful here. The y-intercept of the line with a positive slope is 2 (where the line goes through the y-axis). You figure the slope using rise/run. This line goes up 2 units and over to the right 1 unit, so 2/1 is 2. The slope is 2. The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y intercept. Fill in what you know now. y = 2x + 2. That line is a solid line so it is a "greater than or equal to" situation. Now pick a point on either side of the line and see which, if any, of the equations given to you are satisfied with that point you chose. I picked (-2, 2) to test it out. When I fill in the values for x and y, I do satisfy the equation\[y \ge2x+2\]because 2 is greater than 2(-2) + 2 which is -2. So that's one of the lines. The equation that is paired with that one is y < -x-1. That means that this line intercepts the y axis at -1 and has a slope of -1. That's the other line on the graph you posted. Pick a point and try it anyway, say (-2, -1). If those values make that inequality statement true, then you are sure that that is the right choice for the answer.