Math Problem Statement

Complete the table for the equation x + 2y = 6, and graph the equation.

Solution

The image shows a table that corresponds to the equation x+2y=6x + 2y = 6, with a request to complete the table and graph the equation.

The table has two entries:

  • When x=0x = 0, y=3y = 3 is provided.
  • When y=0y = 0, we need to find xx.

Let's solve for xx when y=0y = 0:

Given the equation: x+2y=6x + 2y = 6

Substitute y=0y = 0: x+2(0)=6x + 2(0) = 6 x=6x = 6

Now, we can complete the table:

  • When x=0x = 0, y=3y = 3 (already given).
  • When y=0y = 0, x=6x = 6.

The completed table looks like this:

\hline x & y \\ \hline 0 & 3 \\ 6 & 0 \\ \hline \end{array}$$ For the graph, you can plot the points $$(0, 3)$$ and $$(6, 0)$$, and draw a straight line through these points to represent the equation. Would you like more details or have any questions about this? Here are 5 related questions you might want to explore: 1. How do you determine the slope of a line from two points? 2. What are the intercepts of the line, and what do they represent? 3. How would you rewrite the equation $$x + 2y = 6$$ in slope-intercept form? 4. What is the significance of solving for $$y$$ when $$x = 0$$ and vice versa? 5. How can you use a graph to verify the solution of an equation? **Tip**: When graphing linear equations, always find at least two points and draw a line through them. This ensures accuracy when representing the equation visually.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

x + 2y = 6

Theorems

Linear equation theory

Suitable Grade Level

Grades 6-8