FOM 5.04a Fit A Line to Data Day 1

5.04a Fit a Line to Data Day 1

Today you will complete this Wayground activity interpreting what the slope and y intercept mean in context given a real world situation.

Open Ended

Why is it important to be able to interpret the line of best fit equation in the context of real-world data?

Multiple Choice

Which of the following keywords are commonly associated with the y-intercept in a linear equation?

• initial

• rate

• average rate of change

• per

Match

Read the scenario and then match the following:​

​

• $5 Per Hour
• $3 Flat Fee

• y=5x+3

• $28

• Linear

Slope

Y-Intercept

Equation

Money Made After 5 Hours

Type of Equation

• Slope

• Y-Intercept

• Equation

• Money Made After 5 Hours

• Type of Equation

Multiple Choice

The function V(t) = 22,000 - 3,400t models the value of Mr. Smith’s boat t years after he purchased it in 2009. What does the 22,000 represent?

• the current value of the boat

• the value of the boat when Mr. Smith purchased it

• the amount the value of the boat increases each year Mr. Smith owns it

• the amount the value of the boat decreases each year Mr. Smith owns it

Multiple Choice

A lawn service company uses the function f(x) = 2.5x + 25 to determine the cost for x hours of service. What does the constant term in the equation represent?

• the total number of hours of lawn service provided

• the initial fee the company charges before providing lawn service

• the total cost for the lawn service

• the cost per hour of lawn service

Multiple Choice

A taxi company uses the function f(x) = 0.45x + 3.50 to determine the cost to take a taxi x miles. What is the meaning of the coefficient of x?

• the cost per mile

• the number of miles

• the total cost to ride a taxi

• the fixed fee the company charges

Multiple Choice

A pizza restaurant charges a flat fee for a plain cheese pizza. There is an extra charge for any additional toppings. The cost of a pizza can be determined from the equation C = 0.5m + 5, where m is the number of additional toppings and C is the cost of the pizza ordered. What are the interpretations of slope and y-intercept in the equation?

• slope: cost per additional topping y-intercept: cost of the plain pizza

• slope: cost per additional topping y-intercept: cost of the first topping

• slope: cost of the plain pizza y-intercept: cost per additional topping

• slope: ratio of cost of additional topping to the cost of the plain pizza y-intercept: cost of an additional topping

Multiple Choice

Albert invests money in an account that earns a yearly dividend. The amount, A, in his account at the end of t years is given by the equation A = $2,400 + $144t. Which statement is correct?

• $2,544 represents the total amount at the end of t years.

• $2,400 represents the total amount at the end of t years.

• $2,400 represents the dividend earned every year.

• $144 represents the dividend earned every year.

Multiple Choice

Avery and her friends attend a museum. It costs $5 to enter the main exhibit hall, with an added charge of $3 to view each special exhibit. Avery writes an equation that models the total price of visiting the museum as a function of the number of special exhibits they view. What is the slope and y-intercept of Avery's model?

• y-intercept = 0, slope = -2

• y-intercept = 0, slope = 3

• y-intercept = 5, slope = 3

• y-intercept = 5, slope = 8

Open Ended

Across the examples of taxi fare, pizza cost, investment growth, museum entry, and phone bill, what is the general role of the slope and y-intercept in a linear function modeling a real-world scenario?

Multiple Choice

The function C(x) = 0.05x + 49.95 models Shelly's total monthly phone bill when she talks for x minutes in the month. What does the constant term of the function represent?

• the total monthly cost

• the fixed monthly rate

• the number of minutes used

• the cost per minute of a phone call

Multiple Choice

What is the meaning of the coefficient of b in the function c = 0.42b + 25, where c is the charge and b is the number of bricks?

• the delivery charge per load

• the total delivery charge

• the total cost of the bricks

• the cost per brick

Open Ended

Reflecting on the formulas for calculating costs in both brick delivery and car rental, what is the significance of the constant term and the coefficient in these linear functions?

Multiple Choice

What does the constant term in the formula C = 0.5x + 30, where x is the number of miles driven, represent?

• number of miles the car has been driven

• rental cost with 30 miles driven

• rental cost with 0 miles driven

• cost per mile driven

Multiple Select

Which equation is not like the others? Be prepared to explain your answer choice!

• A: y = 3.56x - 2

• B: y = 2400 + 144t

• C: y = 1.345x + 4

• D: y = -1.5x + 0.125

Open Ended

Reflecting on today's lesson about fitting a line to data, what is one thing you learned about interpreting the line of best fit equation?