Relate Tables, Graphs, and Equations 2024

Front

What does the equation w = 50m represent in a real-world context?

Back

It represents the relationship between the number of words (w) Nancy can write and the number of minutes (m) she writes, indicating she writes 50 words per minute.

Front

How do you identify the independent variable in a function?

Back

The independent variable is the one that is manipulated or changed in an experiment or equation, often represented on the x-axis in a graph.

Front

What is the dependent variable in the equation y = x - 6?

Back

The dependent variable is y, as its value depends on the value of x.

Front

What is the purpose of completing a table in relation to an equation?

Back

Completing a table helps to visualize the relationship between the independent and dependent variables by showing corresponding values.

Front

What does the term 'rule' refer to in mathematical functions?

Back

The 'rule' refers to the operation or formula that defines how to calculate the output (dependent variable) from the input (independent variable).

Front

If the rule is to multiply by 3, what would be the output if the input is 4?

Back

The output would be 12, as 4 multiplied by 3 equals 12.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the rate of change between the independent and dependent variables, showing how much y changes for a unit change in x.

Front

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

Back

You can plot the independent variable on the x-axis and the dependent variable on the y-axis, creating points that represent the relationship.

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

What does it mean for two variables to be directly proportional?

Back

Two variables are directly proportional if they increase or decrease together at a constant rate, represented by a linear equation through the origin.