Tables, Equations, and Graphs of Functions

Student Summary

Here is the graph showing Noah's run.

A graph in the coordinate plane.
A graph in the coordinate plane, horizontal, distance in meters, 0 to 24 by threes, vertical, time in seconds, 0 to 10 by ones. The graph begins at the origin and steadily increases as it moves right, passing through the labeled point at ( 18 comma 6 ).

The time in seconds since he started running is a function of the distance he has run. The point (18,6)(18,6) on the graph tells us that the time it takes him to run 18 meters is 6 seconds. The input is 18 and the output is 6.

The graph of a function is all the coordinate pairs, (input, output), plotted in the coordinate plane. By convention, we always put the input first, which means that the inputs are represented on the horizontal axis, and the outputs are represented on the vertical axis.

Visual / Anchor Chart

Standards

Addressing
8.F.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line. Recognize examples of functions that are linear and non-linear.