Question

Explaining Your Solution
Explain how you found the equation that represents Aunt Andrea’s decorating plans from the table.

Answer 1

I don’t see the table you’re using — could you paste it? — but here’s a clear step‑by‑step method you can use on any table to find the equation for Aunt Andrea’s decorating plans, plus a short example.

Steps
1. Identify the variables. Decide which column is the independent variable x (often number of items, days, etc.) and which is the dependent variable y (cost, total decorations, etc.).
2. Check whether the relationship is linear. Compute successive differences in y. If the differences are constant, the relationship is linear and has the form y = mx + b.
3. Find the slope m. Choose two table entries (x1,y1) and (x2,y2) and compute m = (y2 − y1) / (x2 − x1).
4. Find the y‑intercept b. Use one ordered pair and solve b = y − m x.
5. Write the equation y = m x + b and check it by plugging in other table pairs to make sure it matches.

Example
Table:
x: 1, 2, 3, 4
y: 5, 8, 11, 14

1. Differences in y: 8−5 = 3, 11−8 = 3, 14−11 = 3 → constant so linear.
2. Slope m = 3 (from the differences).
3. Use (1,5): b = 5 − 3(1) = 2.
4. Equation: y = 3x + 2.
5. Check: x=4 → y = 3(4)+2 = 14, matches the table.

If the first differences are not constant, check second differences: if second differences are constant the pattern is quadratic (y = ax^2 + bx + c). If neither, the table might follow a different type of function and you’ll need a model that fits the pattern.

If you share your specific table I’ll produce the exact equation and show the checks.