For this problem, we are provided two points and we need to determine the equation for the line in standard form.
The standard form of a line is given by:
[tex]Ax+By=C[/tex]
However, it is best to find another variation first, like the point-slope form shown below:
[tex]y-y_p=m\cdot(x-x_p)[/tex]
Where "m" is the slope, and (xp, yp) are the coordinates of a known point on the line. We can find the slope as shown below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}\\ \\ m=\frac{-2+2}{-1+6}=\frac{0}{5}=0 \end{gathered}[/tex]
The slope of the line is equal to 0, which means that it is a line parallel to the "x" axis. This means that the value of B is 0. The full expression is shown below:
[tex]\begin{gathered} y+2=0\cdot(x+6) \\ y+2=0 \\ y=-2 \\ y+0\cdot x=-2 \end{gathered}[/tex]
The expression of the line in standard form is y+0x=-2.
