Question

What is the equation of the line that passes through (-1, -4) and (-2, 3)?

Answer 1

`y=-7x-11`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where m represents the slope and `(x_1,y_1)" a point on the line"`

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 (-1 ,-4) and (-2 ,3)

let `(x_1,y_1)=(-1,-4)" and " (x_2,y_2)=(-2,3)`

`rArrm=(3-(-4))/(-2-(-1))=7/-1=-7`

Using either of the 2 given points for `(x_1,y_1)`

`"Using " (-1,-4)" and " m=-7" then"`

`y-(-4)=-7(x-(-1))`

`rArry+4=-7(x+1)larrcolor(red)"equation in point-slope form"`

Distributing and simplifying this equation, gives us an alternative version for the equation of the line.

`y+4=-7x-7`

`rArry=-7x-11larrcolor(red)" equation in slope-intercept form"`