Question

What is the equation in point-slope form of the line passing through (3, 6) and (−2, 1)?

Answer 1

The point slope formula:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

We have:

`(3,\ 6)\to x_1=3,\ y_1=6\\\\(-2,\ 1)\to x_2=-2,\ y_2=1`

Substitute:

`m=(1-6)/(-2-3)=(-5)/(-5)=1`

`y-6=1(x-3)\\\\y-6=x-3`

Answer 2

Answer: The equation in point slope form is y-6 = x-3

Step-by-step explanation: The general equation of a line in point slope form is y - y1 =m(x -x1)

where m is the slope and (x1,y1) is the point

Given point (3,6) and (-2,1)

We know slope of a line when two points are given

m=
`(y2-y1)/(x2-x1)`

where (x1,y1) and (x2,y2) are the two points

Here m=
`(1-6)/(-2-3)`

=
`(-5)/(-5)`

m=1

Now the equation of line

y-6 = 1 (x-3)

i.e. y-6 = x-3