Comparing Linear Functions

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 linear function represent?

Back

The slope (m) of a linear function 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 in a linear function?

Back

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

Front

How do you determine if two linear functions are parallel?

Back

Two linear functions are parallel if they have the same slope (m) but different y-intercepts (b).

Front

How do you determine if two linear functions are perpendicular?

Back

Two linear functions are perpendicular if the product of their slopes is -1. This means if one slope is m, the other slope must be -1/m.

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 can you convert a linear 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 table?

Back

A function table is a table that displays pairs of input (x) and output (y) values for a function, showing how the output changes with the input.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) is associated with exactly one output (y). A relation can have multiple outputs for a single input.