When graphing a linear inequality, when can you not use (0, 0) as a test point to determine which side of a boundary line to shade?

when the point (0, 0) is on the boundary line.
when the point (0, 0) is below the boundary line.
when the point (0, 0) is above the boundary line.
when the point (0, 0) is part of the solution.

1. When the point (0, 0) is on the boundary line.

Step-by-step explanation:

We know that,

'Zero Test' states that 'After substituting the point (0,0) in the inequality, if the result is true, then the solution region is towards the origin. If the result is false, then the solution region is away from the origin'.

So, we see that,

This test holds only if the point (0,0) does not lie on the boundary line of the inequality.

Since, then the expression 'towards the origin and away from the origin' will not make sense.

Hence, (0,0) cannot be used as test point if it lies on the boundary line.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be