Math Problem Statement
Construct a table of values for the following equation as shown. x=y-3 for integral values of y from -2 to 6
Solution
To construct a table of values for the equation , we will substitute the integral values of from -2 to 6 into the equation and find the corresponding -values.
Here is the table of values:
\hline y & x = y - 3 \\ \hline -2 & -2 - 3 = -5 \\ -1 & -1 - 3 = -4 \\ 0 & 0 - 3 = -3 \\ 1 & 1 - 3 = -2 \\ 2 & 2 - 3 = -1 \\ 3 & 3 - 3 = 0 \\ 4 & 4 - 3 = 1 \\ 5 & 5 - 3 = 2 \\ 6 & 6 - 3 = 3 \\ \hline \end{array}$$ ### Table: | $$y$$ | $$x = y - 3$$ | |--------|-----------------| | -2 | -5 | | -1 | -4 | | 0 | -3 | | 1 | -2 | | 2 | -1 | | 3 | 0 | | 4 | 1 | | 5 | 2 | | 6 | 3 | Would you like a deeper explanation or have any further questions? Here are five related questions you might explore: 1. How would the table change if the equation was $$x = y + 3$$? 2. What is the geometric interpretation of the equation $$x = y - 3$$? 3. What happens to the values of $$x$$ if $$y$$ takes negative non-integer values? 4. Can you find an equation where $$y$$ is expressed in terms of $$x$$? 5. How would you plot this table of values on a coordinate plane? **Tip:** When solving linear equations, always remember the slope-intercept form $$y = mx + b$$, as it helps you understand the relationship between $$x$$ and $$y$$.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Table of Values
Formulas
x = y - 3
Theorems
-
Suitable Grade Level
Grades 6-8