Graphs, Graphing Equations and Inequalities Assignment Help

Introduction to Graphs, Graphing Equations and Inequalities:

Graph:

A graph is depicted in diagrammatic form as asset of dots for the vertices joined by line or curve. It is a representation of set of object where some object are connected by the links. Vertices are the interconnected objects.

Types of graphs:

Distinction in terms of the main definition

Undirected graph
Directed graph
Mixed graph
Multi-graph
Quiver
Simple graph
Weighted graph
Half-edges, loose edges

Important graph classes

Regular graph
Complete graph
Finite and infinite graphs
Graph classes in terms of connectivity
Category of all graphs

Graphing with slope-intercept:

y=(-1)/3 x+2

1. Start by graphing the y-intercept (b = 2).

2. From the y-intercept, apply rise over run using your slope. rise = 1, run = -3

3. Repeat this again from your new point.

4. Draw a line through your points.

Graphing Linear Inequalities:

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:

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

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

3. Shade above the line for a "greater than" (y> or y) or below the line for a "less than " (y< or y).

Example for inequality:

Equation: y 2x-1

The inequality already has "y" on the left and everything else on the right, so no need to rearrange Plot y=2x-1

Shade the area below (because y is less than or equal to)