Relate Tables, Graphs, and Equations

Front

What is the relationship between tables, graphs, and equations?

Back

Tables, graphs, and equations are different ways to represent the same mathematical relationship. A table shows values, a graph visualizes the relationship, and an equation provides a formula to calculate values.

Front

What is an INDEPENDENT variable?

Back

An independent variable is the variable that is changed or controlled in an experiment to test its effects on the dependent variable. In a graph, it is usually plotted on the x-axis.

Front

Which axis on a graph represents the INDEPENDENT variable?

Back

The x-axis represents the independent variable.

Front

What does the point (2, 94) represent in a savings context?

Back

The point (2, 94) means that after 2 weeks, they have saved $94.

Front

What is the algebraic equation for the relationship shown in a table where y decreases as x increases?

Back

The equation could be in the form of y = x - 3, indicating a linear relationship where y decreases as x increases.

Front

How do you identify the dependent variable in a table or graph?

Back

The dependent variable is the one that depends on the independent variable. It is usually plotted on the y-axis.

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 graph?

Back

The slope represents the rate of change between the independent and dependent variables. It shows how much y changes for a change in x.

Front

What is 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 is 0.

Front

How can you convert a table of values into a graph?

Back

To convert a table into a graph, plot each pair of values (x, y) on the graph and connect the points to visualize the relationship.