Linear Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input, meaning no x-value is repeated.

Tags

CCSS.8.F.A.1

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of the y-value with respect to the x-value, calculated as rise over run.

Tags

CCSS.8.EE.B.5

Front

How can you determine if a set of points represents a function?

Back

A set of points represents a function if no x-value is repeated among the points.

Tags

CCSS.8.F.A.1

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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.

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if there are multiple outputs for a single input, meaning at least one x-value is repeated.

Tags

CCSS.8.F.A.1

Front

What is the difference between a linear function and a nonlinear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a nonlinear function does not have a constant rate of change and can graph as a curve.

Tags

CCSS.8.F.A.3

Front

What is the formula for calculating 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 significance of the x-intercept in a linear function?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation y = mx + b.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and calculate slope as rise/run.

Tags

CCSS.8.EE.B.5