Question

How do you write an equation of a line going through (-2,-3), (2,-1)?

Answer 1

`y=1/2x-2`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
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)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

`"the 2 points here are "(-2,-3)" and " (2,-1)`

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

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

`rArry=1/2x+blarr" is the partial equation"`

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

`"using " (2,-1)`

`-1=(1/2xx2)+brArrb=-2`

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