Composing a linear formula

Linear formulas and equations: Linear functions

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 $\blue a=\frac{y_B-y_A}{x_B-x_A}$
Step 4	Enter the found $\blue a$ and $\green b$ in the formula $y=\blue a \cdot x +\green b$ .

Intercept is not readable

It is not always possible to see which $y$ -value corresponds with $x=0$ . In those cases, another way to calculate the value $\green{b}$ is by using two points on the line. We will explain that in Composing the equation of a line.

Create the formula of the linear formula corresponding to the following graph.

The formula is equal to $y=-3 \cdot x + 4$ .

We can calculate this as follows.
Step 1: The intercept $b$ is the $y$ -value of the intersection point of the line and the $y$ -axis. In this case, it 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 now calculate slope $a$ . Here, $a=\tfrac{y_B-y_A}{x_B-x_A}=\tfrac{-2-4}{2-0}=\tfrac{-6}{2}=-3$

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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