Question

Slope is -5 and (2, 1) is on the line; standard form

Answer 1

We have to find the equation of the line in standard form, knowing that the slope is m = -5 and it passes through the point (2, 1).

The standard form is:

`Ax+By=C`

When we know the slope and one point, we can write the equation in slope-point form. Then, we can rearrange the terms in order to find the standard form.

The slope-point form is:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-1=-5(x-2) \end{gathered}`

We then can rearrange it as:

`\begin{gathered} y-1=-5(x-2) \\ y=-5x-5\cdot(-2)+1 \\ y=-5x+10+1 \\ y+5x=11 \\ 5x+y=11 \end{gathered}`

Answer: the standard form of the line is 5x + y = 11.