Question

How do you write an equation in standard form for a line which passes through points (-1,-1) and (1,3)?

Answer 1

`2x-y=-1`

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"`

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

`•color(white)(x)y=mx+b`

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

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

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

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

`m=(3-(-1))/(1-(-1))=4/2=2`

`y=2x+blarrcolor(blue)"is the partial equation"`

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

`"using "(1,3)" then"`

`3=2+brArrb=3-2=1`

`y=2x+1larrcolor(red)"in slope-intercept form"`

`"rearranging gives"`

`2x-y=-1larrcolor(red)"in standard form"`