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.