Question

How do you write the equation of a line given (6,1) (-3,-2)?

Answer 1

`y=1/3x-1`

Explanation:

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

`color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))`
where m represents the slope and b, the y-intercept.

To obtain the equation ,we require to find m and b.

m can be calculated using 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 points"`

let `(x_1,y_1)=(6,1)" and " (x_2,y_2)=(-3,-2)`

`rArrm=(-2-1)/(-3-6)=(-3)/(-9)=1/3`

Partial equation is `y=1/3x+b`

To find b , substitute one of the 2 given points into the partial equation, say (-3 ,-2)

x = -3 , y = -2 gives.

`-2=(1/3xx-3)+b→-2=-1+b→b=-1`

`rArry=1/3x-1" is the equation of the line"`
graph{1/3x-1 [-10, 10, -5, 5]}