Question

How do you write the equation in point slope form given (3,8) and (9,0)?

Answer 1

`y-8=-4/3(x-3)`

Explanation:

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

`•color(white)(x)y-y_1=m(x-x_1)`

`"where m is the slope and "(x_1,y_1)" a point on the line"`

`"to calculate m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(3,8)" and "(x_2,y_2)=(9,0)`

`rArrm=(0-8)/(9-3)=(-8)/6=-4/3`

`"using "(x_1,y_1)=(3,8)" as a point on the line then"`

`y-8=-4/3(x-3)larrcolor(red)"in point-slope form"`

Answer 2

See a solution step below..

Explanation:

Recall the equation of a line is;

`y = mx + c`

Where;

`m = "slope"`

Also recall that;

`m = (y₂ - y_1)/(x₂ - x_1)`

where;

`y₂ = 0`

`y_1 = 8`

`x₂ = 9`

`x_1 = 3`

substituting the values

`m = (0 - 8)/(9 - 3)`

`m = -8/6`

`m = -4/3`

using these points `(3, 8)` to get the slope form..

`y - y_1 = m (x - x_1)`

Therefore;

`y - 8 = -4/3 (x - 3)`

As required..