Consider the table of values.



Which could be the equation representing these values?

Responses

y = 2 x − 3

y = 2 ⁢ x + 3



In order to determine which equation represents the table of values, we need to compare the equations to the values in the table. I'll guide you through the process:

### Step 1: Understand the two possible equations
1. \( y = 2x - 3 \)
2. \( y = 2x + 3 \)

### Step 2: Check how the equations behave

For each \( x \)-value from the table, plug the value of \( x \) into both equations and see which one gives the corresponding \( y \)-value in the table.

- For the first equation \( y = 2x - 3 \), we calculate:
  - \( y(1) = 2(1) - 3 = -1 \)
  - \( y(2) = 2(2) - 3 = 1 \)
  - \( y(3) = 2(3) - 3 = 3 \)
  
- For the second equation \( y = 2x + 3 \), we calculate:
  - \( y(1) = 2(1) + 3 = 5 \)
  - \( y(2) = 2(2) + 3 = 7 \)
  - \( y(3) = 2(3) + 3 = 9 \)

### Step 3: Match the table values
Check which of the two results match the corresponding \( y \)-values in the table.

If you provide the table of values, I can confirm which of the two equations represents it.

Would you like to provide the table of values so I can match the correct equation?

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### 5 Relative Questions:
1. How do you identify the slope of a line from an equation like \( y = 2x - 3 \)?
2. What role does the y-intercept play in determining the equation of a line?
3. How can you determine whether a table of values follows a linear or quadratic pattern?
4. What methods can be used to find the equation of a line from a table of values?
5. How can you graph an equation given a set of values from a table?

### Tip:
Always check if the difference between consecutive \( y \)-values is constant; this indicates a linear relationship.

Consider the table of values. Which could be the equation representing these values? y = 2x − 3 or y = 2x + 3.

Learn how to determine the correct linear equation from a table of values using two possible equations: y = 2x − 3 and y = 2x + 3. This problem covers key algebraic concepts, including slope-intercept form and understanding linear relationships. Suitable for students in Grades 6-8.

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