# COMPARING A TABLE AND AN EQUATION WORKSHEET

## About "Comparing a table and an equation worksheet"

Comparing a table and an equation worksheet :

Worksheet on comparing a table and an equation is much useful to the students who would like to practice problems on "Describing functions".

## Comparing a table and an equation worksheet - Problems

1.  David and John buy MP3 files from different music services. The monthly cost, y dollars, for x songs is linear. The cost of David’s service is y = 0.50x + 10. The table given below shows the cost of John’s service.

2.  Alex is choosing between buying books at the bookstore or buying online versions of the books for his tablet. The cost, y dollars, of ordering books online for x books is ya=a6.95xa+a1.50. The cost of buying the books at the bookstore is shown in the table. Which method of buying books is more expensive if Quentin wants to buy 6 books ?

## Comparing a table and an equation worksheet - Solution

Problem 1 :

David and John buy MP3 files from different music services. The monthly cost, y dollars, for x songs is linear. The cost of David’s service is y = 0.50x + 10. The table given below shows the cost of John’s service.

Based on the information given above, compare the services of David and John.

Solution :

Step 1 :

To compare the services of David and John, let us have both the services as equations. David's service is already given as equation. So, let us write John's service as equation.

Choose any two ordered pairs from the table to find the slope.

Let us use the ordered pairs (5, 4.95) and (10, 9.90).

Slope m  =  (y₂ - y) / (x₂ - x)

Slope m  =  (9.90 - 4.95) / (10 - 5)

Slope m  =  4.95 / 5

Slope m  =  0.99

Step 2 :

Find the y-intercept. Use the slope and any point.

Slope-intercept form equation of a line.

y  =  mx + b

Plug m  =  0.99, x  =  5 and y  =  4.95.

4.95  =  0.99 · 5 + b

4.95  =  4.95 + b

Subtract 4.95 from both sides.

0  =  b

Step 3 :

Substitute the slope and y-intercept.

y  =  0.99x + 0

y  =  0.99x

Step 4 :

To compare the services, find the cost in both the services when 30 songs are downloaded.

That is, find the values of "y" in the equations when x = 30.

David's service

y  =  0.50 · 30 + 10

y  =  25

John's service

y  =  0.99 · 30

y  =  29.7

Hence, David's service is cheaper..

Problem 2 :

Alex is choosing between buying books at the bookstore or buying online versions of the books for his tablet. The cost, y dollars, of ordering books online for x books is ya=a6.95xa+a1.50. The cost of buying the books at the bookstore is shown in the table. Which method of buying books is more expensive if Quentin wants to buy 6 books ?

Solution :

Step 1 :

To know which method of buying books is more expensive if Quentin wants to buy 6 books, let us have both the methods as equations. Buying books online is already given as equation. So, let us write buying books at the store as equation.

Choose any two ordered pairs from the table to find the slope.

Let us use the ordered pairs (1, 7.50) and (2, 15.00).

Slope m  =  (y₂ - y) / (x₂ - x)

Slope m  =  (15.00 - 7.50) / (2 - 1)

Slope m  =  7.50 / 1

Slope m  =  7.50

Step 2 :

Find the y-intercept. Use the slope and any point.

Slope-intercept form equation of a line.

y  =  mx + b

Plug m  =  7.50, x  =  1 and y  =  7.50

7.50  =  7.50 · 1 + b

7.50  =  7.50 + b

Subtract 7.50 from both sides.

0  =  b

Step 3 :

Substitute the slope and y-intercept.

y  =  7.50x + 0

y  =  7.50x

Step 4 :

To know which method of buying books is more expensive if Quentin wants to buy 6 books, find the values of y in the equations when x = 6.

y  =  6.95 · 6 + 1.50

y  =  43.20

y  =  7.50 · 6

y  =  45

Hence, buying books at the book store is expensive.

After having gone through the stuff given above, we hope that the students would have understood "Comparing a table and an equation worksheet".

Apart from the stuff given on "Comparing a table and an equation worksheet", if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6