# How to Complete a Table and Graph a Two-Variable Equation?

Welcome to this step-by-step guide on how to complete a table and graph a two-variable equation!

By following this guide, you'll gain a comprehensive understanding of the process and be able to apply it to various mathematical problems. ## A step-by-step guide tocomplete a table and graph a two-variable equation

Here is a step-by-step guide on how to complete a table and graph a two-variable equation:

1. Identify the two variables in the equation: The two variables in a two-variable equation are typically represented by $$x$$ and $$y$$. Identify which variables are involved in your equation.
2. Choose values for $$x$$: Choose a set of values for x that are meaningful and representative of the problem or situation. It’s often helpful to choose a range of values that span the relevant domain of $$x$$.
3. Substitute the chosen values of $$x$$ into the equation: For each chosen value of $$x$$, substitute it into the equation and solve for $$y$$. This will give you the corresponding value of y for that particular value of $$x$$.
4. Record the $$x-y$$ pairs in a table: Record each pair of $$x$$ and $$y$$ values in a table with two columns labeled “$$x$$” and “$$y$$”. Be sure to label each row with the corresponding value of $$x$$.
5. Plot the points on a graph: Create a coordinate plane by drawing two perpendicular axes labeled “$$x$$” and “$$y$$”. Plot each point from the completed table on the graph by locating its $$x$$ and $$y$$ values on the axes and marking it with a point.
6. Connect the points with a line or curve: After plotting all the points on the graph, connect them with a line or curve that best fits the data. The shape of the line or curve depends on the nature of the equation. For example, a linear equation will have a straight line, while a quadratic equation will have a curve.
7. Label the graph: Be sure to label the axes with their corresponding variables ($$x$$ and $$y$$) and include a title that describes the equation and what the graph represents.
8. Analyze the graph: Once the graph is complete, analyze it to determine any patterns or trends in the data. Look for relationships between $$x$$ and $$y$$, such as positive or negative correlations. The graph can also be used to make predictions and extrapolations about the data beyond the range of values included in the table.

### Complete a Table and Graph a Two-Variable Equation – Example 1

Complete the table. Then graph the equation.
$$y=2x$$

#### Solution:

Put the value of $$x$$ into the equation and calculate $$y$$ to find the $$y$$-value.
$$y=2×1=2, y=2×2=4, y=2×3=6 y=2×4=8$$
Write the values in the table as ordered pairs: $$(1:2),(2:4),(3:6),(4:8)$$
So,

Now, graph $$(1:2),(2:4),(3:6),(4:8)$$.

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