Question

is there an easier way to find standard form when dealing with graphing

Answer 1

Given a graph, you need two points to determine the equation of the line in standard form.

The standard form of a line is :

$Ax+By=C$

If you already have two points on the line, you can use the two point formula :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

For example, if you have the points (1, 3) and (4, 6)

The equation will be :

$y-3=\frac{6-3}{4-1}(x+1)$

Simplify and rewrite in standard form.

$\begin{gathered} y-3=\frac{3}{3}(x+1) \\ y-3=x+1 \\ -x+y=1+3 \\ -x+y=4 \\ x-y=-4 \end{gathered}$

The equation in standard form is x - y = -4