Compare Linear Functions (Tables, Graphs, and Equations)

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.

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 the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

How do you find the slope from a table of values?

Back

To find the slope from a table of values, select two points (x1, y1) and (x2, y2) and use the formula: slope (m) = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

Front

How can you determine if one linear function has a greater slope than another?

Back

Compare the slope values (m) of the two functions. The function with the larger slope value has a greater slope.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

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 graph a linear function using its equation?

Back

To graph a linear function, identify the y-intercept (b) and plot it on the y-axis. Then use the slope (m) to find another point by rising and running from the y-intercept.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward line. A negative slope indicates that as x increases, y decreases, resulting in a downward line.

Tags

CCSS.8.EE.B.5

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. They will never intersect.

Tags

CCSS.8.EE.B.5

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 one slope is the negative reciprocal of the other.

Tags

CCSS.8.EE.B.6