Final answer:
To match the table with the correct equation, each x value is substituted into the four given equations. Only the equation C) y = 4x - 3 produces the y values that match those in the table for every x value. Therefore, equation C is the one that matches the given table.
Step-by-step explanation:
The student has asked to determine which equation matches the given table containing values for x and y. The key to solving this problem is to identify an equation whose pattern fits the pairings of x and y values in the table. Given the options, we need to apply the values from the table to each equation to see which one correctly reflects the relationship between x and y.
Looking at the table, when x = 0, y = -3. When x = 2, y = 5. When x = 3, y = 9. When x = 4, y = 13. These pairs suggest a consistent pattern of change, which can help us identify the correct equation. Let's apply the x values from the table to each of the given equations to find the one that consistently produces the matching y-values:
- A) y = x - 3: If you plug in x = 0, y will be -3, which matches the table. Let's check another value. If x = 2, y would be -1, which does not match the table.
- B) y = x + 3: If you plug in x = 0, y will be +3, which does not match the table.
- C) y = 4x - 3: If x = 0, y = -3; if x = 2, y = 5; if x = 3, y = 9; if x = 4, y = 13. Each of these calculations matches the table.
- D) y = 4x + 3: Starting with x = 0, y will be 3, which does not match the table.
Based on this analysis, we can conclude that the correct equation is C) y = 4x - 3.