Topic 3: Linear Functions (enVision Algebra 1)

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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What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

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What is the y-intercept?

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 do you find the line of best fit for a set of data points?

Back

To find the line of best fit, you can use statistical methods such as least squares regression, which minimizes the sum of the squares of the residuals.

Front

What is a residual in the context of linear functions?

Back

A residual is the difference between the actual y-value and the predicted y-value from the line of best fit.

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What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

How do you determine the common difference in an arithmetic sequence?

Back

The common difference is found by subtracting any term from the subsequent term in the sequence.

Front

What is the formula for the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

In an arithmetic sequence, the difference between consecutive terms is constant, while in a geometric sequence, the ratio between consecutive terms is constant.

Front

What does it mean for a sequence to be linear?

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A sequence is linear if it can be represented by a linear function, meaning the change between terms is consistent and can be graphed as a straight line.