Question

In which graph does the shaded region represent the solution to the inequality:

Answer 1

Graph A

Step-by-step explanation:

Given the inequality:

`y+x<1-x`

Combining like terms:

`\begin{gathered} y+x+x<1 \\ y+2x<1 \\ \implies y<-2x+1 \end{gathered}`

Since the sign is less than (<), the graph that represents this inequality must be shaded below the boundary line.

However, the coefficient of x when the inequality is written in slope-intercept form is negative, so the line must have a negative slope.

The correct choice is Graph A.