Question

How do you write an equation in standard form for a line passing through (3, –6) and (–2, –1)?

Answer 1

`x+y=-3`

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"`

`"to begin obtain the equation in "color(blue)"slope-intercept form"`
`"and rearrange into standard form"`

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"calculate m using the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(3,-6)" and "(x_2,y_2)=(-2-1)`

`rArrm=(-1-(-6))/(-2-3)=5/(-5)=-1`

`rArry=-x+blarrcolor(blue)"is the partial equation"`

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

`"using "(3,-6)" then"`

`-6=-3+brArrb=-6+3=-3`

`rArry=-x-3larrcolor(red)"in slope-intercept form"`

`"add "x" to both sides"`

`rArrx+y=-3larrcolor(red)"in standard form"`