GOZUNTA
Try it now
All courses Math Foundations · MF.GR.7 46 of 60
Match and compare words, tables, graphs, and simple equations that represent the same relationship.

Match a table to its rule

Problem
A table maps \(x\)-values \(0,~1,~2,~3\) to \(y\)-values \(2,~6,~10,~14\). Determine the equation represented by the table.
Relationship Table: x and y with 4 rows. 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

Read the steps or watch the work.

Every problem included with your free account keeps its hints, complete written solution, and step-by-step learning video available for review.

Create a free account
With paid access

Try the same skill with new numbers.

More variants let you check whether you understand the method instead of remembering one answer.

Compare plans

Hint

Look at the row where x = 0 to find the starting value, then check how much y increases each time x goes up by 1.

A table and an equation match only if they have the same starting value and the same rate of change.

Solution walkthrough

01

Read the table pairs

\[(x,y)=(0,2),(1,6),(2,10),(3,14)\]

The inspected table supplies consecutive x-values and their outputs.

02

Find the rate of change

\[(6-2)/(1-0)=4;~(10-6)/(2-1)=4;~(14-10)/(3-2)=4\]

Every one-unit increase in x raises y by four, so the coefficient is four.

03

Find the starting value

\[x=0~⇒~y=2~⇒~b=2\]

The zero-input row gives the constant term in y=mx+b.

04

Build and check the equation

\[y=4x+2;~x=3~⇒~4(3)+2=14\]

Combining rate four and start two reproduces the final row.

05

Report the equation

\[y~=~4x~+~2\]

The equation represents both the constant rate and starting value in the table.

+

Another way

  1. Assume y=mx+b, use (0,2) for b, then use (1,6) to solve 6=m+2.

!

Common mistake

Do not write y=4x and omit the starting value; the table gives y=2 when x=0.

Solution walkthrough video