Question

use the equation to draw a line in the graphx + y < - 8

Answer 1

Consider the given expression,

$x+y<-8$

This is a strict inequality, whose boundary is formed by a straight line.

At least two points are needed to plot the line on the Cartesian Plane.

Put x=0 in the eqiation,

$\begin{gathered} 0+y=-8 \\ y=-8 \end{gathered}$

So the line passes through (0,-8).

Put y=0 in the equation,

$\begin{gathered} x+0=-8 \\ x=-8 \end{gathered}$

So the line passes through (-8,0).

Check if (0,0) is a solution of the inequality,

$\begin{gathered} 0+0<-8 \\ 0<-8 \end{gathered}$

This is a false statement as 0 cannot be less than -8, so (0,0) is not in the solution region.

The graph of the inequality is obtained as follows,