Question

How do you write an equation of a line given (1,-3) and (-2,-4)?

Answer 1

`y=1/3x-10/3`

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 points"`

`"the points are " (x_1,y_1)=(1,-3),(x_2,y_2)=(-2,-4)`

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

`rArry=1/3x+blarr" is partial equation"`

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

`"using " (1,-3)`

`-3=1/3+brArrb=-3-1/3=-10/3`

`rArry=1/3x-10/3larrcolor(red)" in slope-intercept form"`