Question

Study the table representing the price of different amounts of apples, in pounds, and then complete the sentences.

The constant difference in the y-values is
.

The linear function is

Answer 1

I don’t see the table — could you paste the x (amount of apples) and y (price in pounds) values here?

Meanwhile, here’s how to get the two answers from the table:

1. Constant difference in the y-values:
- Subtract consecutive y-values (y2 − y1, y3 − y2, ...). If the differences are all equal, that common value is the constant difference in y.
- If x-steps are not 1, compute the slope m = (change in y) / (change in x). If x-steps are 1, m equals the constant y-difference.

2. Linear function:
- The slope m is the constant difference per 1 unit of x (or computed as above).
- Find the intercept b by plugging one table pair (x0, y0) into y = mx + b and solving b = y0 − m x0.
- The linear function is y = m x + b (y in pounds).

Example: if the table were
x: 0, 1, 2
y: £0, £1.20, £2.40
then the constant y-difference = £1.20, m = 1.20, and y = 1.20x.

Send the table values and I’ll give the exact constant difference and the linear function.