Real World Linear Equations

Front

What does the equation y = -25x + 120 represent in a real-world context?

Back

It represents a situation where there are 120 gallons of water in a tank, and it releases water at a rate of 25 gallons per minute.

Front

What is the equation for total charges at Easy Car Rental for x hours?

Back

y = 25.5 + 8.5x

Front

How do you find the time when a plane reaches a certain altitude using the equation a = 3400t + 600?

Back

Set a equal to the desired altitude and solve for t. For example, to find when the plane is at 21,000 feet, solve 21,000 = 3400t + 600.

Front

What does 'b' represent in the equation y = mx + b?

Back

'b' represents the initial value or y-intercept of the line.

Front

Write the equation for the total cost (C) of towing a vehicle for m miles if the flat fee is $50 and the cost per mile is $8.

Back

C = 8m + 50

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

If a car rental service charges a flat fee plus a per hour rate, how would you express the total cost?

Back

Total cost = flat fee + (hourly rate * number of hours) or y = b + mx.

Front

How can you interpret the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

Front

What is the significance of the slope in a real-world scenario?

Back

The slope indicates how much y changes for a unit change in x, representing rates like speed, cost per item, etc.

Front

How do you determine the total cost of a service that has a fixed fee and a variable cost?

Back

Add the fixed fee to the product of the variable cost per unit and the number of units.