Multiple Representations

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 represented by the value of b in the equation y = mx + b.

Front

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

Back

To determine the equation of a line from a table, find the rate of change (slope) between the x and y values, and then use one of the points to find the y-intercept.

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

How do you identify the equation from a graph?

Back

To identify the equation from a graph, determine the slope and y-intercept from the graph, then use the slope-intercept form y = mx + b.

Front

What is the relationship between x and y in the equation y = 3x?

Back

In the equation y = 3x, for every unit increase in x, y increases by 3 units. This shows a direct proportional relationship.

Front

What does the term 'input' refer to in a function?

Back

The term 'input' refers to the value you put into a function, usually represented by x in the equation y = f(x).

Front

What does the term 'output' refer to in a function?

Back

The term 'output' refers to the value you get from a function after applying the input, usually represented by y in the equation y = f(x).

Front

How can you represent a relationship between two variables?

Back

A relationship between two variables can be represented using an equation, a table of values, or a graph.