I see you've uploaded a page with questions on trend line equations. Let's go through each of the parts:

Part A: Trend Line Equations

1. Write an equation for the trend line. From the graph, it appears the equation for the trend line is given as: $y = 2x + 60$ This suggests that the slope of the line is 2 and the y-intercept is 60.

2. Predict the score of a student who studies for 30 minutes. Using the equation $y = 2x + 60$ where $x = 30$: $y = 2(30) + 60 = 60 + 60 = 120$ So, the predicted score for a student studying 30 minutes is 120. However, this result might be above the typical scale (out of 100), which could indicate that there might be a need for adjustments in interpretation or boundary constraints.

3. Trenton still needs to take the exam and wants to score a 100. How many minutes should he plan to study? We need to set $y = 100$ and solve for $x$ in the equation $y = 2x + 60$: $100 = 2x + 60$ Subtract 60 from both sides: $40 = 2x$ Now, divide both sides by 2: $x = 20$ Trenton should plan to study for 20 minutes.

Part B: Project Research Data

4. The trend line equation is $y = -15x + 100$. This equation is true, based on the given graph of the scatter plot. The negative slope indicates that as the number of days increases, the percentage of the project remaining decreases.

5. A student who has worked on the project for 5 days should have about 25% of the project remaining. Let's substitute $x = 5$ into the equation $y = -15x + 100$: $y = -15(5) + 100 = -75 + 100 = 25$ So, this statement is true.

6. A student who has 10% of the project remaining has likely spent about 9 days working on the project. Let's substitute $y = 10$ into the equation: $10 = -15x + 100$ Subtract 100 from both sides: $-90 = -15x$ Divide both sides by -15: $x = 6$ This statement is false. It would take 6 days, not 9, for the student to have 10% remaining.

Part C: Fast Food Restaurant Data

7. If Miguel waits 6 minutes in line to order, predict the number of employees working. The equation given is $y = -1.5x + 15$, where $y$ is the number of minutes and $x$ is the number of employees. We substitute $y = 6$ into the equation: $6 = -1.5x + 15$ Subtract 15 from both sides: $-9 = -1.5x$ Divide both sides by -1.5: $x = 6$ So, there are 6 employees working.

8. Joni arrives at the restaurant when 8 employees are working. Predict the amount of time she will wait to order. Substitute $x = 8$ into the equation $y = -1.5x + 15$: $y = -1.5(8) + 15 = -12 + 15 = 3$ Joni will wait 3 minutes.

Would you like more details on any of these answers? Let me know if you need further clarification!

Here are 5 related questions for deeper exploration:

1. How does the slope of a trend line impact the interpretation of data in real-world situations?
2. What is the significance of the y-intercept in a trend line equation?
3. How do you interpret trend lines when predicting outcomes beyond the scope of given data?
4. Can the equation $y = 2x + 60$ represent a non-linear relationship between study time and score? Why or why not?
5. How might you adjust trend lines if data points start showing significant outliers?

Tip: Always double-check your predictions by substituting values back into the original equation to verify the accuracy of your solution!