Question

Which graph shows the solution to the system of linear inequalities? y>2/3x+3

Answer 1

Answer:

Graph attached.

Step-by-step explanation:

y > $\frac{2}{3}$x + 3

When x = 0 , y = 3

When y = 0 , x = -4.5

Graphing the two points (0, 3) and (-4.5, 0) gives the graph attached below:

The shaded part is the wanted region.

Answer 2

Step-by-step explanation:

Graphing Linear Inequalities

This is a graph of a linear inequality:

linear inequality y <= x +2

The inequality y ≤ x + 2

You can see the y = x + 2 line, and the shaded area is where y is less than or equal to x + 2

Linear Inequality

A Linear Inequality is like a Linear Equation (such as y = 2x+1) ...

... but it will have an Inequality like <, >, ≤, or ≥ instead of an =.

How to Graph a Linear Inequality

First, graph the "equals" line, then shade in the correct area.

There are three steps:

Rearrange the equation so "y" is on the left and everything else on the right.

Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)

Shade above the line for a "greater than" (y> or y≥)

or below the line for a "less than" (y< or y≤).

Let us try some examples:

Example: y≤2x-1

1. The inequality already has "y" on the left and everything else on the right, so no need to rearrange

2. Plot y=2x-1 (as a solid line because y≤ includes equal to)