Question

How to write an equation in standard form for a line through (4,3); slope 1/2?

Answer 1

`x-2y=-2`

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"`

`"here "m=1/2`

`y=1/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(4,3)" into the partial equation"`

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

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

`"multiply through by 2"`

`2y=x+2`

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