# 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:

### 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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