Question

How do you write an equation in standard form given point (3,3) and (1,-3)?

Answer 1

`3x-y=6`

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, are integers.

`"express the equation initially in "color(blue)"slope-intercept form"`

`• y=mx+b`

#"where m represents the slope and b the y-intercept.

`"to calculate m use the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
`(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

`"the points are " (x_1,y_1)=(3,3),(x_2,y_2)=(1-3)`

`rArrm=(-3-3)/(1-3)=(-6)/(-2)=3`

`rArry=3x+blarr" is the partial equation"`

`"to find b substitute either of the 2 points into the"`
`"partial equation"`

`"using " (3,3)`

`3=9+brArrb=-6`

`rArry=3x-6larrcolor(red)" in [slope-intercept form](https://socratic.org/algebra/graphs-of-linear-equations-and-functions/slope-intercept-form)"`

`"rearrange equation into standard form"`

`rArr3x-y=6larrcolor(red)" in standard form"`