GOZUNTA
Try it now
All courses Algebra I · F-LE.1.b 29 of 76
Recognize constant rate of change as evidence for a linear model.

Find constant rate of change from a table

Problem
Use the displayed \(x\text{-}y\) table. Compute the signed interval rate or rates and answer the constant-rate question.
Clean source table or point graph without solution cues. Open full size
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
With a free account

Let your results add up.

Each saved attempt adds useful evidence about what you have practiced and what deserves another pass.

Create a free account
With paid access

Use the screen to choose. Use paper to solve.

Build the exact session you want online, then export it as a printable worksheet.

Compare plans

Hint

Use two consecutive points, such as (0, 5) and (2, 11), and compute change in output over change in input: (11 - 5)/(2 - 0).

Constant rate of change means change in output divided by change in input. Divide the output change by the input change, and keep the units as output units per input unit.

Solution walkthrough

01

Read two consecutive table points

\[(0,5)~\text{and}~(2,11)\]

These are the first two points in the inspected table. Input is x and output is y.

02

Compute signed changes

\[\text{change}~\text{in}~\text{output}=11-5=6;~\text{change}~\text{in}~\text{input}=2-0=2\]

Both changes are positive because both coordinates increase from the first point to the second.

03

Form the interval rate

\[\text{rate}=(\text{change}~\text{in}~\text{output})/(\text{change}~\text{in}~\text{input})=6/2=3\]

Dividing output change by input change gives 3 output units for each one input unit. The later table interval also gives (17-11)/(4-2)=3, checking constancy.

04

State the rate with units

\[3~\text{output}~\text{units}~\text{per}~\text{input}~\text{unit}\]

The positive sign means the output increases, and the units state the required output-per-input interpretation.

+

Another way

  1. Use the first and last inspected points: (17-5)/(4-0)=12/4=3.

!

Common mistake

Do not report the output change 6 alone. A rate divides that change by the corresponding input change 2.

Worked answer representation with the requested signed rate, completion, or diagnosis.
3 output units per input unit

Solution walkthrough video