Math Problem Statement

Copy and complete the table for the graph of 2x - y = 8. The table includes x-values of -2, -1, 0, 1, and 2, and you need to fill in the corresponding y-values (A, B, and C).

Solution

To complete the table, we can solve for yy in terms of xx using the given equation 2xy=82x - y = 8.

  1. Rearrange the equation to express yy: y=2x8y = 2x - 8

  2. Now, plug in the given values of xx to find yy:

  • When x=2x = -2: y=2(2)8=48=12(This is value A)y = 2(-2) - 8 = -4 - 8 = -12 \quad \text{(This is value A)}

  • When x=0x = 0: y=2(0)8=08=8(This is value B)y = 2(0) - 8 = 0 - 8 = -8 \quad \text{(This is value B)}

  • When x=2x = 2: y=2(2)8=48=4(This is value C)y = 2(2) - 8 = 4 - 8 = -4 \quad \text{(This is value C)}

Completed table:

xx-2-1012
yy-12-10-8-6-4

Let me know if you need more details or have any questions.

Relative questions:

  1. How do you graph a line using the slope-intercept form?
  2. What happens to the graph if the equation changes to 2xy=52x - y = 5?
  3. Can you explain how to find the slope of the line from the equation 2xy=82x - y = 8?
  4. How would you solve the equation for xx given a value for yy?
  5. What does the intercept mean in this linear equation?

Tip: Always check your rearranged equation to make sure it's in the correct form before substituting values.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra
Solving for y

Formulas

2x - y = 8
y = 2x - 8

Theorems

Linear equation theory

Suitable Grade Level

Grades 6-8