# How to Complete a Graph and Table Linear Function

A linear function is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Linear functions are of the form \(y=mx+b\), where \(m\) and \(b\) are constants.

## A Step-by-step Guide to Completing a Graph and Table Linear Function

Completing a graph and table for a linear function involves following these steps:

### Step 1: Understanding the Equation

To start with, you need to understand the equation of the linear function. In the equation \(y=mx+b\), \(“m”\) represents the slope of the line (which determines its angle of inclination), and \(“b”\) is the \(y\)-intercept (where the line crosses the \(y\)-axis).

### Step 2: Creating a Table of Values

Next, create a table of values for \(x\) and \(y\). Choose a range of values for \(x\) and then calculate the corresponding \(y\) values using your equation. For example, if your equation is \(y=2x+3\), and you choose \(x\) values of \(-1, 0,\) and \(1,\) your \(y\) values would be \(1, 3,\) and \(5\) respectively.

Here’s what that table would look like:

x | y |

-1 | 1 |

0 | 3 |

1 | 5 |

### Step 3: Plotting the Graph

After creating a table of values, you can plot these values on a graph. The \(x\)-values represent the horizontal position, and the \(y\)-values represent the vertical position. Plot each \((x, y)\) point on the graph and then draw a straight line that passes through these points. Remember that for a linear function, all the points will fall on the same line.

### Step 4: Completing the Graph

After you’ve plotted the points and drawn a line through them, your graph is complete. Make sure to label your axes and, if necessary, include a legend that explains what the line represents.

### Step 5: Interpreting the Graph and Table

Lastly, you can use your graph and table to understand more about your linear function. The graph can show you visually how \(y\) changes with changes in \(x\). The slope and \(y\)-intercept that you identified from the equation are represented visually in the graph: the slope as the incline of the line and the \(y\)-intercept as the point where the line crosses the \(y\)-axis. The table gives you specific pairs of \(x\) and \(y\) values and can be used to calculate further values if necessary.

That’s a basic rundown of how to complete a graph and table for a linear function. This process is fundamental to algebra and is an essential tool for understanding and representing linear relationships.

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