REPRESENTING LINEAR RELATIONSHIPS USING TABLES

We can use an equation to describe the linear relationship between two quantities in a real-world situation. We can use a table to show some values that make the equation true.

Example 1 : 

The equation y = 3x + 2 gives the total charge for one person, y, renting a pair of shoes and bowling x games at Baxter Bowling Lanes based on the prices shown. Make a table of values for this situation.

Solution :

Step 1 :

Choose several values for x that make sense in context.

x  =  1, 2, 3, 4

Step 2 :

Use the equation y = 3x + 2 to find y for each value of x.

x  =  1 :

y  =  3(1) + 2

y  =  3 + 2

y  =  5

x  =  2 :

y  =  3(2) + 2

y  =  6 + 2

y  =  8

x  =  3 :

y  =  3(3) + 2

y  =  9 + 2

y  =  11

x  =  4 :

y  =  3(4) + 2

y  =  12 + 2

y  =  14

Step 3 :

Let us list out the values of y for the corresponding values of x using a table.

Example 2 : 

Francisco makes $12 per hour doing part-time work on Saturdays. He spends $4 on transportation to and from work. The equation y = 12x - 4 gives his earnings y, after transportation costs, for working x hours. Make a table of values for this situation.

Solution :

Step 1 :

Choose several values for x that make sense in context.

x  =  1, 2, 3, 4

Step 2 :

Use the equation y = 12x - 4 to find y for each value of x.

x  =  1 :

y  =  12(1) - 4

y  =  12 - 4

y  =  8

x  =  2 :

y  =  12(2) - 4

y  =  24 - 4

y  =  20

x  =  3 :

y  =  12(3) - 4

y  =  36 - 4

y  =  32

x  =  4 :

y  =  12(4) - 4

y  =  48 - 4

y  =  44

Step 3 :

Let us list out the values of y for the corresponding values of x using a table.

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