Matching Equations to tables and graphs

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How do you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify two points on the line, calculate the slope (m), and use one of the points to find the y-intercept (b).

Front

What is the relationship between equations and tables?

Back

Equations can be used to generate tables of values, and tables can be used to derive equations by identifying patterns in the data.

Front

How can you match an equation to a table of values?

Back

To match an equation to a table, substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they represent the same line on a graph, meaning they have the same slope and y-intercept.

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.

Front

How do you convert an equation from slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).