Math Problem Statement

Construct a table of values for the following equation: x = y - 4 for integral values of y from -5 to +3. Complete the following table of values.

Solution

The equation given in the image is x=y−4x = y - 4, and you are asked to create a table of values for integral values of yy from -5 to 3. Let's solve this step by step by substituting the values of yy into the equation to find the corresponding values of xx.

Equation:

x=y−4x = y - 4

Values of yy:

y=−5,−4,−3,−2,−1,0,1,2,3y = -5, -4, -3, -2, -1, 0, 1, 2, 3

Substituting each value of yy into the equation:

  1. For y=−5y = -5, x=−5−4=−9x = -5 - 4 = -9
  2. For y=−4y = -4, x=−4−4=−8x = -4 - 4 = -8
  3. For y=−3y = -3, x=−3−4=−7x = -3 - 4 = -7
  4. For y=−2y = -2, x=−2−4=−6x = -2 - 4 = -6
  5. For y=−1y = -1, x=−1−4=−5x = -1 - 4 = -5
  6. For y=0y = 0, x=0−4=−4x = 0 - 4 = -4
  7. For y=1y = 1, x=1−4=−3x = 1 - 4 = -3
  8. For y=2y = 2, x=2−4=−2x = 2 - 4 = -2
  9. For y=3y = 3, x=3−4=−1x = 3 - 4 = -1

Completed Table of Values:

\hline y & x \\ \hline -5 & -9 \\ -4 & -8 \\ -3 & -7 \\ -2 & -6 \\ -1 & -5 \\ 0 & -4 \\ 1 & -3 \\ 2 & -2 \\ 3 & -1 \\ \hline \end{array}$$ Let me know if you need more details or have any questions! --- ### Related Questions: 1. What is the slope of the equation $$x = y - 4$$? 2. Can you rewrite the equation $$x = y - 4$$ in slope-intercept form? 3. What would the table look like if the equation was $$x = y + 2$$? 4. How would the graph of this equation look on a Cartesian plane? 5. What happens to $$x$$ as $$y$$ increases by 1? ### Tip: When working with linear equations, it's helpful to recognize the pattern between the variables. In this case, every time $$y$$ increases by 1, $$x$$ also increases by 1.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Substitution
Coordinate Geometry

Formulas

x = y - 4

Theorems

Linear Equation Properties

Suitable Grade Level

Grades 7-9

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