Question

What is the point-slope form of the line that passes through (5,6) and (3,10)?

Answer 1

`y-6=-2(x-5)`

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)=(5,6)" and "(x_2,y_2)=(3,10)`

`m=(10-6)/(3-5)=4/(-2)=-2`

`"use either of the 2 given points as a point on the line"`

`"using "(x_1,y_1)=(5,6)" then"`

`y-6=-2(x-5)larrcolor(red)"in point-slope form"`