Real World Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes 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

What does the slope of a line represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the total cost in a linear cost model?

Back

The total cost can be found using the equation C = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

If a plumber charges a flat fee plus an hourly rate, how can this be modeled with a linear equation?

Back

The total cost can be modeled as C = hourly_rate * hours + flat_fee.

Front

What is the purpose of using ordered pairs in linear equations?

Back

Ordered pairs (x, y) are used to represent solutions to linear equations, showing the relationship between x and y.

Front

How can you determine if an ordered pair is a solution to a linear equation?

Back

Substitute the x and y values of the ordered pair into the equation. If both sides of the equation are equal, it is a solution.

Front

What is the significance of the flat fee in a service charge model?

Back

The flat fee is a fixed cost that does not change with the number of hours worked or distance traveled.

Front

How do you set up a linear equation from a word problem?

Back

Identify the variables, determine the fixed and variable costs, and express the relationship in the form of a linear equation.

Front

What is the formula to calculate total revenue from ticket sales?

Back

Total revenue can be calculated as Total Revenue = Price per ticket * Number of tickets sold.