6.3 Applications of Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that represents a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you write an equation for total cost based on fixed and variable costs?

Back

The total cost (c) can be expressed as c = fixed cost + (variable cost per unit * number of units).

Front

If a driving range charges a fixed fee and a variable fee per bucket of balls, how would you express the total cost?

Back

c = 2.75b + 4, where c is the total cost and b is the number of buckets.

Front

How do you solve for the number of buckets if the total cost is known?

Back

Rearrange the equation to isolate b: b = (c - fixed cost) / variable cost per unit.

Front

What is the formula to calculate the total cost of a trip based on a base fare and a per-mile charge?

Back

Total cost = base fare + (per-mile charge * distance traveled).

Front

How do you calculate the price before a percentage reduction?

Back

Price before reduction = final price / (1 - percentage reduction).

Front

What is the equation to find the total amount spent by two people if one spends less than twice the other?

Back

Let x be the amount spent by the first person. The second person spends 2x - amount less. Total = x + (2x - amount less).

Front

How do you set up an equation for a plumber's charges based on a service call and hourly rate?

Back

Total cost = service call fee + (hourly rate * hours worked).

Front

What is the total cost for 2.5 hours of labor if the hourly rate is $25?

Back

Total cost = $50 (service call) + ($25 * 2.5) = $112.50.

Front

How do you find the total amount spent by two people if their combined spending is known?

Back

Set up an equation: total = amount spent by person A + amount spent by person B.