Question

How do you write an equation of a line that passes through points (4,2), (-2,-4)?

Answer 1

`y=x-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 t-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 are " (x_1,y_1)=(4,2),(x_2,y_2)=(-2,-4)`

`rArrm=(-4-2)/(-2-4)=(-6)/(-6)=1`

`rArry=x+blarr" partial equation"`

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

`"using " (4,2)`

`2=4+brArrb=-2`

`rArry=x-2larrcolor(red)" in slope-intercept form"`
graph{x-2 [-10, 10, -5, 5]}