**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.

After having gone through the stuff given above, we hope that the students would have understood, how to represent linear relationships using tables".

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