Question

Which equation represents the line that passes through (6, 7) and (3, 6)?

Answer 1

`y=1/3x+5`

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 (6 ,7) and (3 ,6)

let `(x_1,y_1)=(6,7)" and " (x_2,y_2)=(3,6)`

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

`"Using " m=1/3" and " (x_1,y_1)=(3,6)`

substitute values into equation.

`y-6=1/3(x-3)rArry-6=1/3x-1`

`rArry=1/3x+5" is the equation"`