First of all, using the information about constant rate we can say that these points are located on a straight line. Indeed, the logic is about a constant rate. Then, we can easily claim that the points are located on a quasi-linear function, y=kx+b. We could solve this problem by setting up a system of equations. The system is this:
By solving it, we find that k=0.5 and b=12. Then the function is y=0.5x+12
We have to find that how many rows were completed, before Elene started, i.e, x = 0. Then y=0.5*0+12 = 12. The answer is 12 rows.
The answer is 12. :)
The graph that accompanies this question is in the figure attached.12
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 formy - 22 = 0.5 (x - 20)y = 0.5x - 10 + 22y = 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.