Question

Elena agrees to finish a knitting project for a friend. The graph shows the number of rows Elena completes compared to the amount of time spent knitting.


Assuming she worked at a constant rate, how many rows had been completed before Elena started working?

12
14
15
19



In order for the data in the table to represent a linear function with a rate of change of –8, what must be the value of a?

a = 2
a = 3
a = 19
a = 35

Answer 1

I don’t have the graph or the table you’re referring to, so I can’t pick the numeric answers yet. If you can either upload the graph/table or type the relevant points, I’ll solve both parts.

Here is how I’ll solve each as soon as you provide the data:

1) Knitting graph (constant rate)
- Read two clear points from the line (x1, y1) and (x2, y2), where x = time and y = rows.
- Compute the rate (slope) m = (y2 − y1) / (x2 − x1).
- Compute the rows completed before she started (the y‑intercept) with b = y1 − m·x1 (this is the value at time x = 0).
- The y‑intercept b is the number you choose from the list (12, 14, 15, 19).

2) Table with required rate of change −8
- Identify two entries in the table that include the unknown a (or give the full table).
- Use (y2 − y1) / (x2 − x1) = −8 and solve for a.
- That will produce one of the choices (2, 3, 19, 35).

If you paste the graph points or the table values (or upload an image), I’ll compute the answers step by step.