Relating Equations & Tables

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?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (upward or downward).

Front

What is the y-intercept in a linear equation?

Back

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

Front

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

Back

To determine the equation from a table, look for patterns in the values of x and y. Calculate the slope (change in y/change in x) and use a point to find the y-intercept.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that you can control or change (usually x), while the dependent variable is the one that depends on the independent variable (usually y).

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line when graphed.

Front

What is a function?

Back

A function is a relation where each input (x) has exactly one output (y). It can be represented by an equation, a table, or a graph.

Front

How can you identify a function from a set of ordered pairs?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

What is the purpose of graphing a linear equation?

Back

Graphing a linear equation helps visualize the relationship between the variables and can show solutions to the equation.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.