Multiple Representations

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you calculate the total cost of a service with a fixed fee and a variable charge?

Back

The total cost can be calculated using the equation: Total Cost = Fixed Fee + (Variable Charge per unit * Number of units).

Front

What does the slope of a linear equation represent in a real-world context?

Back

The slope represents the rate of change or the cost per unit in a real-world context.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0; it represents the starting value in a real-world scenario.

Front

How can you represent a relationship between two variables using a function?

Back

A relationship can be represented using a function by defining one variable in terms of another, such as W(t) = 10t for earnings based on hours worked.

Front

What is the significance of the equation y = mx + b in graphing?

Back

This equation allows you to graph a straight line, where m is the slope and b is the y-intercept.

Front

How do you determine the equation of a line from a table of values?

Back

You can determine the equation by identifying the pattern in the changes of y with respect to x, often resulting in a linear relationship.

Front

What is a real-world example of a linear function?

Back

A real-world example is calculating total earnings based on hourly wage and hours worked, such as W(t) = 10t.

Front

How do you interpret the coefficients in a linear equation?

Back

Coefficients indicate the rate of change; for example, in y = 0.15x + 40, 0.15 is the cost per minute and 40 is the base fee.

Front

What is the relationship between a graph and its corresponding equation?

Back

The graph visually represents the equation, showing how the dependent variable changes with the independent variable.