Key Concepts

• A linear function can be graphed by making a table of inputs and outputs then plotting them as points on a coordinate plane, then drawing a line between them.
• The slope of the graph of a linear function can be calculated given any two ordered pairs [latex]\left(x, f(x)\right)[/latex].
• The slope of the graph of a linear function by examining whether the function values rise, fall, or remain constant as the function input increases.
• The units for the rate of change are given in a ratio of input units over output units.
• The slope of the graph of a linear function represents the rate of change in the function values over a given change in input.

Glossary

average rate of change

the slope of a line between two points on the graph of a function, calculated via a ratio of the change in function output over the corresponding change in function input

ordered pair

a coordinate pair of input and output, [latex]\left(x, f(x)\right)[/latex]

slope

a measurement of the steepness of a line graphed in the plane.

slope-intercept form

[latex]y=mx+b[/latex]