Linear formulas and equations: Linear functions
Composing a linear formula
Composing a linear formula
Procedure 

With a graph or table of a linear formula, we can compose a formula of the form #y=\blue a \cdot x +\green b# in the following manner. 

Step 1 
Determine intercept #\green b# by seeing which #y#value corresponds with #x=0#. 
Step 2 
Pick two "nice" or convenient points #A# and #B# with coordinates #\rv{x_A, y_A}# and #\rv{x_B, y_B}#. 
Step 3 
Calculate slope #a# with \[\blue a=\frac{y_By_A}{x_Bx_A}\] 
Step 4 
Enter the found #\blue a# and #\green b# in the formula #y=\blue a \cdot x +\green b#. 
The formula is equal to #y=3 \cdot x + 4#.
We can calculate this as follows.
Step 1: The starting number #b# is the #y#value of the intersection point of the #y#axis. In this case, that is #4#.
Step 2: We choose two grid points, for example #A# with coordinates #\rv{0,4}# and #B# with coordinates #\rv{2,2}#
Step 3: We will now calculate slope #a#. Here #a=\tfrac{y_By_A}{x_Bx_A}=\tfrac{24}{20}=\tfrac{6}{2}=3#
Step 4: We can now substitute the found values for #a# and #b# in the formula #y=a \cdot x+b#. The formula therefore becomes #y=3 \cdot x + 4#.
We can calculate this as follows.
Step 1: The starting number #b# is the #y#value of the intersection point of the #y#axis. In this case, that is #4#.
Step 2: We choose two grid points, for example #A# with coordinates #\rv{0,4}# and #B# with coordinates #\rv{2,2}#
Step 3: We will now calculate slope #a#. Here #a=\tfrac{y_By_A}{x_Bx_A}=\tfrac{24}{20}=\tfrac{6}{2}=3#
Step 4: We can now substitute the found values for #a# and #b# in the formula #y=a \cdot x+b#. The formula therefore becomes #y=3 \cdot x + 4#.
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