Question

How do you write the equation in point slope form given (0,9) and (2,0)?

Answer 1

`y=-9/2x+9`

Explanation:

the slope is given by `m=(y_2-y_1)/(x_2-x_1)` and this is `m=-9/2`
for the equation `y=-9/2x+n` we get `n`: as `9`

Answer 2

`y=-9/2(x-2)`

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)=(0,9)" and "(x_2,y_2)=(2,0)`

`m=(0-9)/(2-0)=(-9)/2=-9/2`

`"using "m=-9/2" and "(x_1,y_1)=(2,0)`

`y-0=-9/2(x-2)larrcolor(red)"in point-slope form"`

`"or "y=-9/2(x-2)`