Equation of the line
There are several forms to express the equation of a line.
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The standard form of a line is:
Ax + By = C
We are given two points (1,2) and (3,10). The point-point equation is adequate according to the data we are provided.
[tex]\begin{gathered} \displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ \text{Substituting:} \\ \displaystyle y-2=\frac{10-2}{3-1}(x-1) \end{gathered}[/tex]Operating:
[tex]\begin{gathered} y-2=\frac{8}{2}(x-1)=4(x-1) \\ \\ \text{Operating:} \\ y-2=4x-4 \end{gathered}[/tex]Subtracting 4x and adding 2:
y - 4x = -4 + 2 = -2
Rearranging:
-4x + y = -2
This is the required equation in standard form
