Constant Rate Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Determine whether the data is consistent with a constant rate of change: x:0,2,4,6x: 0, 2, 4, 6 and y:3,7,12,15y: 3, 7, 12, 15. If not, find where it fails.

Solution

  1. 1
    Compute rates: (7−3)/(2−0)=2(7-3)/(2-0)=2; (12−7)/(4−2)=2.5(12-7)/(4-2)=2.5; (15−12)/(6−4)=1.5(15-12)/(6-4)=1.5.
  2. 2
    The rates 22, 2.52.5, 1.51.5 are not constant. The data does not represent a linear function; the rate of change varies.

Answer

Not constant rate; rates are 22, 2.52.5, 1.51.5
Constant rate of change requires equal differences in yy for equal differences in xx (constant slope). Checking successive slopes diagnoses non-linearity. This data has an irregular rate, inconsistent with a linear model.

About Constant Rate

A constant rate of change means the output increases (or decreases) by the same fixed amount for every unit increase in the input — the hallmark of a linear function.

Learn more about Constant Rate →

More Constant Rate Examples

Example 1 easy

A car travels at a constant speed of [formula] km/h. Write the distance function [formula], find [fo

Example 2 medium

Find the equation of the line passing through [formula] and [formula], interpret the slope, and writ

Example 3 easy

A plumber charges a [formula]50[formula][formula] per hour. Write [formula] and find the cost for [f

← All Constant Rate Examples Constant Rate Concept