elena agrees to finish a knitting project for a friend. the graph shows the number of rows elena completes…
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? rows vs. time 12 14 15 19
Answer
Explanation:
Step1: Find the slope of the line
The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(14,19)$ and $(20,22)$: $m=\frac{22 - 19}{20 - 14}=\frac{3}{6}=\frac{1}{2}$
Step2: Use the point - slope form of a line $y - y_1=m(x - x_1)$
Using the point $(14,19)$ and $m = \frac{1}{2}$, we have $y-19=\frac{1}{2}(x - 14)$. Expanding gives $y-19=\frac{1}{2}x-7$, so $y=\frac{1}{2}x + 12$.
Step3: Find the y - intercept
The y - intercept represents the number of rows completed before starting. When $x = 0$, $y=12$.
Answer:
12