Question

Which system of linear inequalities is graphed? {y>2x+1x+y<−2 {y<2x+1x+y>−2 {y≤2x+1x+y≥−2 {y≥2x+1x+y≤−2 The image is a system of linear inequalities graphed on a coordinate plane with increments of 1 and x and y axis ranging from negative 5 to 5. A dashed line passes through the points begin ordered pair 0 comma 1 end ordered pair and begin ordered pair 1 comma three end ordered pair. The shading is above the line. The other line passes through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 2 comma zero end ordered pair. The shading is below this line.

Answer 1

Let us check the slope of y-intercepts of the given lines in the graph first.

The y-intercept of above line is 1 and slope of

Rise/run = 2/1 (Moving 2 units up and 1 unit right).

So, the equation should be

y=2x+1

Y-intercept of second line is -2 and slope is

Rise/run = -1/1 (Moving 1 unit down and 1 unit right).

So, the equation should be

y=-x-2.

Now, we need to check the shaded portion for inequality signs.

We have both lines dotted.

So, the inequality signs would be just < or >.

For y=2x+1 line : Shading is on the left side.

On the left side of the line y=2x+1, the y-values are greater than on right side.

Therefore, we got first inequality y>2x+1

For y=-x-2 line : Shading is on the down of the line.

On the down of the line y=-x-2, the y-values are less than up side of the line.

Therefore, second inequality would be

y<-x-2 or y+x<-2

Therfore, correct option is first option y>2x+1 and y+x<-2.