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Linear Functions: Medium 🔒

How well can you connect slope, intercepts, and real-world rates? Work through problems that ask you to interpret, compare, and build linear functions.

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Question 1
A line passes through the points \((2, -1)\) and \((6, 11)\). What is the equation of this line in slope-intercept form?
🔒 Answer question 1 to unlock
A reservoir contains 800,000 gallons of water. Due to a drought, water is released at a constant rate, and after 10 days the reservoir holds 650,000 gallons. If the release rate stays the same, after how many total days will the reservoir hold 500,000 gallons?
🔒 Answer question 2 to unlock
Two phone plans are modeled by the functions below, where \(x\) is the number of gigabytes of data used per month. \[\begin{aligned} \text{Plan A:} \quad C &= 5x + 20 \\ \text{Plan B:} \quad C &= 8x + 11 \end{aligned}\] For what value of \(x\) do both plans cost the same?
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A plumber charges a flat service fee plus an hourly rate. The total charge for a 2-hour job is $130 and for a 5-hour job is $250. What is the plumber's hourly rate, in dollars?
🔒 Answer question 4 to unlock
The function \(f(x) = -4x + 200\) models the number of tickets remaining for a concert \(x\) hours after sales open. What does the slope represent in this context?
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