### Linear formulas and equations: Formulas

### Graphs

We can create a **table** corresponding to the formula #\blue{y=5x+10}# :

\[\begin{array}{l|c|c|c|c|c}

x & 0 & 1 & 2 & 3 & 4\\

\hline

y & 10 & 15 & 20 & 25 & 30

\end{array}\] We made this table by calculating the value of #y# corresponding to the chosen value of #x# in the upper row. The values of @y@ are in the bottom row.

We can make a **graph** corresponding to this table. The upper row with values for #x# corresponds to the horizontal axis, and the bottom row with values for #y# corresponds to the vertical axis.

If #x=1#, then #y=15#. This corresponds to the **point **#\rv{1,15}#. On the right you see how you can find this point by drawing perpendicular lines from the axes. From the table it follows that the graph goes through the following points: #\rv{0,10}#, #\rv{1,15}#, #\rv{2,20}#, #\rv{3,25}# and #\rv{4,30}#. These points are drawn on the right and connected by a smooth line, which in this case is a straight line.

#\boldsymbol{x}# | #-4# | #-3# | #-2# | #-1# | #0# | #1# | #2# | #3# | #4# |

#\boldsymbol{y}# | #-284# | #-121# | #-36# | #-5# | #-4# | #-9# | #4# | #59# | #180# |

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