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

Answer 1

12

Step-by-step explanation:

Answer 2

The graph that accompanies this question is in the figure attached.

Answer:

• 12

Step-by-step explanation:

The assumption that Elena worked at a constant rate permits you to build a linear model for the the number of rows Elena completes (dependent variable) in function of the time spent knitting (independent variable).

The coordinates of the points shown on the graph are (14,19), (20,22), and (30,27), and you need to find how many rows had been completed before Elena started working.

The number of rows that had been completed before she started working is the number of rows for time equal 0, which is the y-intercept of the function that models the situation.

Then, what you need to do is to find the equation of the line, using two of the three given points, and then tell the y-intercept.

a) Find the slope, m:

• m = rise / run = Δy / Δx = (22 - 19) / (20 - 14) = 3 / 6 = 1/2 = 0.5

b) Use one point (20, 22) to find the equation of the line:

• y - y₁ = m (x - x₁) ← point-slope form

• y - 22 = 0.5 (x - 20)

• y = 0.5x - 10 + 22

• y = 0.5x + 12 ← slope intercept form

The constant term of the slope-intercept equation, ie. 12, represents the y-intercept. Thus, your answer is 12.