What is the significance of the y-intercept in real-world scenarios?

The y-intercept can represent the starting value of a situation in real-world applications, such as the initial cost before any changes.

How can you determine if a function is linear from a table of values?

If the differences between consecutive y-values are constant for equal differences in x-values, the function is linear.

What is the standard form of a linear equation?

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

What is the relationship between the slope and the angle of a line?

The slope of a line is the tangent of the angle (θ) that the line makes with the positive x-axis.

How do you graph a linear function?

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

What is the difference between a function and a relation?

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

What does it mean for a linear function to be increasing or decreasing?

A linear function is increasing if its slope is positive and decreasing if its slope is negative.

How can you identify the slope and y-intercept from a graph?

The slope can be found by determining the rise over run between two points, and the y-intercept is where the line crosses the y-axis.

Linear Functions Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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

2.

FLASHCARD QUESTION

Front

What does the slope of a linear function represent?

Back

The slope 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

3.

FLASHCARD QUESTION

Front

What is the y-intercept of a linear function?

Back

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

4.

FLASHCARD QUESTION

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Tags

CCSS.8.EE.B.5

5.

FLASHCARD QUESTION

Front

What is the formula for the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

6.

FLASHCARD QUESTION

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Tags

CCSS.8.EE.B.5

7.

FLASHCARD QUESTION

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Tags

CCSS.8.EE.B.5

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