Question

Write the equation in standard form for the line that passes through the given points. (Be sure to simplify and do not put passes between the terms.)

Answer 1

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:

`Ax+By=C`

However, it is best to find another variation first, like the point-slope form shown below:

`y-y_p=m\cdot(x-x_p)`

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:

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1)\\ \\ m=(-2+2)/(-1+6)=(0)/(5)=0 \end{gathered}`

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:

`\begin{gathered} y+2=0\cdot(x+6) \\ y+2=0 \\ y=-2 \\ y+0\cdot x=-2 \end{gathered}`

The expression of the line in standard form is y+0x=-2.