Question

How do you find a standard form equation for the line with (3,1), with slope of m=1/3?

Answer 1

`x-3y=0`

Explanation:

`"the equation of a line in "color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`

`"where A is a positive integer and B,C are integers"`

`"we can obtain the equation in "color(blue)"point-slope form"`

`•color(white)(x)y-y_1=m(x-x_1)`

`"where m is the slope and "(x_1,y_1)" a point on the line"`

`"here "m=1/3" and "(x_1,y_1)=(3,1)`

`rArry-1=1/3(x-3)larrcolor(blue)"in point-slope form"`

`rArry-1=1/3x-1larrcolor(blue)"distributing"`

`rArry=1/3x`

`"multiply through by 3"`

`rArr3y=xrArrx-3y=0larrcolor(red)"in standard form"`

Answer 2

`y=1/3x`

Explanation:

The standard equation is `y=mx+c`

So we have `y=1/3x+c` and it passes through (3,1)

`1=1/3xx3+c` `=>` `1=1+c` so c=0