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All courses Math I · S-ID.6.a 54 of 59
Use scatter plots to represent two quantitative variables and fit functions to model relationships.

Create a scatter plot from paired data

Problem
Specify the scatter plot for (1,2), (2,4), (3,5), and (4,8), using x=input from 0 to 4 by 1 and y=output from 0 to 8 by 1. Include the axes, point set, point count, and a coordinate-order and window check.
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Hint

Write axis labels/ranges, then copy each pair without swapping and reconcile the point count.

A complete non-drawing scatter specification needs labeled axis windows/ticks and every ordered pair exactly once; x is always first.

Solution walkthrough

01

Set and label the coordinate window

\[x=\text{input}~\text{from}~0~\text{to}~4~\text{step}~1;~y=\text{output}~\text{from}~0~\text{to}~8~\text{step}~1\]

The prompt supplies both variable meanings, bounds, and tick increments; x is input and y is output.

02

Preserve ordered-pair meaning

\[(x,y)=(\text{input},\text{output})\]

For every observation, the first coordinate locates the horizontal input and the second locates the vertical output.

03

Plot every observation

\[\text{points}={(1,2),(2,4),(3,5),(4,8)}\]

Each of the four supplied pairs contributes one unconnected scatter point.

04

Check count and bounds

\[\text{count}=4;~0≤x≤4~\text{and}~0≤y≤8~\text{for}~\text{all}~\text{four}~\text{points}\]

All first coordinates fall in the horizontal window and all second coordinates fall in the vertical window, including the boundary point (4,8).

05

State the complete scatter specification

\[\text{axes}=x~\text{input}~[0,4]~\text{step}1;~y~\text{output}~[0,8]~\text{step}1;~\text{points}={(1,2),(2,4),(3,5),(4,8)};~\text{count}=4;~\text{check}=\text{all}~\text{four}~\text{pairs}~\text{lie}~\text{within}~\text{axes}~\text{with}~x~\text{as}~\text{first}~\text{coordinate}\]

This gives the exact axes, points, observation count, coordinate order, and window check required by the prompt.

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Another way

  1. Make an x-y checklist with rows 1/2, 2/4, 3/5, and 4/8, then plot and check off each row once.

!

Common mistake

Do not swap a pair such as (1,2) into (2,1), and do not connect the scatter points. The first coordinate always uses the input axis.