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? the graph is titled rows vs. time. the x - axis is labeled time (minutes) with values 0, 5, 10, 15, 20, 25, 30, 35, 40, 45. the y - axis is labeled rows completed with values 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. the points on the graph are (14, 19), (20, 22), (30, 27). the multiple - choice options are 12, 14, 15, 19.

Explanation:

Step1: Find the slope (rate)

Use two points, e.g., \((14, 19)\) and \((20, 22)\). Slope \(m=\frac{22 - 19}{20 - 14}=\frac{3}{6}=\frac{1}{2}\) rows per minute.

Step2: Find the y-intercept (initial rows)

Use point-slope form \(y - y_1 = m(x - x_1)\) with \((14, 19)\) and \(m=\frac{1}{2}\).
\(y - 19=\frac{1}{2}(x - 14)\)
Simplify: \(y=\frac{1}{2}x - 7 + 19=\frac{1}{2}x + 12\).
When \(x = 0\) (start time), \(y = 12\).

Answer:

12