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.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

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

Front

What is the domain of a linear function?

Back

The domain of a linear function is the set of all possible x-values that can be input into the function, typically all real numbers unless otherwise restricted.

Front

What is the range of a linear function?

Back

The range of a linear function is the set of all possible y-values that the function can output, typically all real numbers unless otherwise restricted.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that if one line has a slope of m, the other line must have a slope of -1/m.

Tags

CCSS.8.EE.B.6

Front

If the slope of a line is 3, what is the slope of a line perpendicular to it?

Back

The slope of a line perpendicular to a line with slope 3 is -1/3.

Tags

CCSS.8.EE.B.6

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 the 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 involving x and y on one side.