### Linear formulas and equations: Formulas

### Formulas

Jack walks with a pace of #5# kilometers per hour. We calculate the distance Jack has walked with the **formula** #\orange{s} = 5 \cdot \blue{t}#.

Here the #\orange{\text{distance}}# is denoted in kilometers with the variable #\orange{s}# and the #\blue{\text{time}}# is denoted in hours with the variable #\blue{t}#. Using this formula, we can calculate the distance #\orange{s}# for different values of time #\blue{t}#.

If Jack walks for #\blue{2}# hours, #\blue{t}=\blue{2}#.

We get #\orange{s}= 5 \cdot \blue{2} = \orange{10}#, so Jack has walked #\orange{10}# kilometers.

If Jack walks for #\blue{4}# hours, #\blue{t}=\blue{4}#.

We get #\orange{s}= 5 \cdot \blue{4} = \orange{20}#, so Jack has walked #\orange{20}# kilometers.

**The formula:**

\[\orange{s} = 5 \cdot \blue{t} \]

If #\blue t=\blue 2#, then #\orange{s}= 5 \cdot \blue{2} = \orange{10}#

If #\blue t=\blue 4#, then #\orange{s}= 5 \cdot \blue{4} = \orange{20}#

The formula is: #k=3.50 \cdot t + 7.00#

The total costs for skating can be calculated by adding the price of the admission ticket to the number of hours multiplied by the price for #1# hour of skating.

In words, the formula looks like this:

\[\textit{total cost skating}=3.50 \cdot \textit{number of hours} + 7.00\]

Using letters for the variables, we can write this formula a little shorter:

\[k=3.50 \cdot t + 7.00\]

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