Linear functions

Connect slope and intercept meanings across formulas, tables, and graphs.

Meaning

In the linear function with is the constant rate of change or slope, and is the vertical-axis intercept. Its graph is a straight line.Changing the input by h changes the output by a(x+h)+b−(ax+b)=ah. The starting value b cancels, leaving the constant rate a per unit of input change.

Example

For increasing by 1 increases by 2; at It passes through and Direct proportion is the special case Not every linear function with an intercept is directly proportional.

Practice for this concept

Scope and references

Topics

Slope, intercepts, graphs, relationships between two lines

Learning goal

Connect slope and intercept meanings across formulas, tables, and graphs.

Helpful background

Revisit substitution, coordinates, and changes in two quantities as needed.

Values and changes in linear functions

Does not ask you to draw graphs or assess the full definition of functions.

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