Linear Functions Study Guide

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.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

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.

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CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you determine if a function is discrete or non-discrete?

Back

A function is discrete if it consists of distinct, separate values (like counting numbers). It is non-discrete if it can take any value within a range (like measurements).

Front

What is the constant of proportionality in a linear relationship?

Back

The constant of proportionality is the coefficient of x in the equation y = kx, where k represents the constant ratio between y and x.

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CCSS.HSF-LE.A.1B

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values in the table.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation is y = 2x + 3.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

If Adam earns $10 for each car he washes, what type of function does this represent?

Back

This represents a discrete function because the number of cars washed can only be whole numbers.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the difference between discrete and continuous data?

Back

Discrete data consists of separate values (like counts), while continuous data can take any value within a range (like measurements).

Front

How do you express a linear relationship in the form y = kx?

Back

To express a linear relationship in the form y = kx, identify the constant ratio between y and x, where k is the constant of proportionality.

Tags

CCSS.HSF-LE.A.1B