Question

I need help with homework question and please help with plotting the points on the graph please it’s highly important for the equation. I have the answer already I just need help plotting the dots on the line. It’s two lines. One line has two points and the second line has two points as well and I already have the outcome but really I stress on placing the coordinates on the line

Answer 1

Given the set of inequalities:

-2x - 2y > 1

y ≥ -2

Let's graph the system of linear inequalities and shade the solution set.

For the first inequality, rewrite in slope-intercept form:

y = mx + b

Add 2x to both sides:

-2x + 2x - 2y > 2x + 1

-2y > 2x + 1

Divide through by 2:

`\begin{gathered} (-2y)/(-2)>(2x)/(-2)+(1)/(-2) \\ \\ y<-x-(1)/(2) \end{gathered}`

Now, let's get two points from this inequality.

When: x = 1.5:

`\begin{gathered} x=1.5 \\ y<-1.5-(1)/(2) \\ y<-2 \\ \\ \\ \text{WHen x = 0} \\ y<-0-(1)/(2) \\ y<-0.5 \end{gathered}`

For the first inequality, we have the points:

(x, y) ==> (1.5, -2), (0, -0.5)

Plot the points and connect the points using a dashed line.

Shade the area below the boundary region since y is less than.

• For the second inequality:

`y\ge-2`

This inequality is a horizontal line at y = -2.

We can get any two points on the line:

(x, y) ==> (4, -2), (1.5, -2)

Draw a dashed line at y = 2.