Question

Which graph represents the inequality y > 1-3x? ​

Answer 1

For this case we must indicate the graph of the following inequality:

$y\geq 1-3x$

It is observed that inequality includes equality, so the boundary line of the graph will not be dotted, so we discard options A and C.

We test option B, we substitute the point (0,0) in the inequality, if it is fulfilled then the graph corresponds to it.

$0 \geq1-3 (0)\\0 \geq1$

It is not fulfilled!

We test the last option, we choose the point (3,1) that belongs to the graph:

$1\geq1-3 (3)\\\1 \geq1-9\\1 \geq-8$

Is fulfilled!

Answer:

Option D

Answer 2

The graph which represents the inequality y ≥ 1-3x is graph D.

To graph the inequality : y ≥ 1-3x

Consider the inequality sign ≥ (this will require a solid line)

< >( uses a dotted line)

Take a point which isn't on the line :

Say (0, 0)

Substitute ist value into the equation :

y ≥ 1-3x

0 ≥ 1 - 3(0)

0 ≥ 1 - 0

0 ≥ 1 (This is false)

This means that the solution does not contain the point (0,0)

Hence, we shade the lower part of the graph which does not contain (0,0)

The correct graph of y ≥ 1-3x is the graph which it's shaded portion does not contain the point (0,0) and it is represented by a solid line.

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