Question

determining the effect of a new initial value
science
jennas science teacher changed the number of assignments for the semester to 85. this is shown as the blue line on the graph.
how many more weeks will it take jenna to complete all the assignments if she completes assignments at the same rate?
more weeks

Explanation:

Step1: Find the rate of completing assignments

First, find the rate using the points $(3,55)$ and $(6,40)$. The rate $r=\frac{55 - 40}{6 - 3}=\frac{15}{3}=5$ assignments per week.

Step2: Find the time to complete the original number of assignments

From the point $(3,55)$, assume the original number of assignments $y$ can be modeled by a linear - relationship. If at week $3$ there are $55$ assignments left, and the rate is $5$ assignments per week, the original number of assignments is $y=55 + 3\times5=70$.

Step3: Find the time to complete the new number of assignments

The new number of assignments is $85$. The time $t_1$ to complete $70$ assignments at a rate of $5$ assignments per week is $t_1=\frac{70}{5}=14$ weeks. The time $t_2$ to complete $85$ assignments at a rate of $5$ assignments per week is $t_2=\frac{85}{5}=17$ weeks.

Step4: Calculate the additional weeks

The additional weeks $=t_2 - t_1=17 - 14 = 3$ weeks.

Answer:

3