Matching Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 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 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 do you determine if a point (x, y) lies on the line of a linear function?

Back

To determine if a point (x, y) lies on the line, substitute x into the linear equation and see if the resulting y value matches the y-coordinate of the point.

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 find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two linear functions to be parallel?

Back

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

Front

What does it mean for two linear functions to be perpendicular?

Back

Two linear functions are perpendicular if the product of their slopes is -1. This means that one slope is the negative reciprocal of the other.

Front

How do you graph a linear function?

Back

To graph a linear function, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through these points.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a two-dimensional space, written in the form (x, y).