Question

How do you write an equation of a line going through (4,-1), (6,-7)?

Answer 1

`y=-3x+11`

Explanation:

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

`color(red)(bar(ul(|color(white)(a/a)color(black)(y-y_1=m(x-x_1))color(white)(a/a)|)))`
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)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))`
where `(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"`

The 2 points here are (4 ,-1) and (6 ,-7)

let `(x_1,y_1)=(4,-1)" and " (x_2,y_2)=(6,-7)`

`rArrm=(-7-(-1))/(6-4)=(-6)/2=-3`

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

We now have `m=-3" and " (x_1,y_1)=(4,-1)`

Substitute these values into the point-slope equation.

`y-(-1)=-3(x-4)rArry+1=-3x+12`

`rArry=-3x+11" is the equation of the line"`