Question

Find an equation of the line containing the given pair of points in​ point-slope form and in​ slope-intercept form.

​(1​,5​) and ​(3​,6​)

Answer 1

Part 1)
`y-5=(1)/(2)(x-1)`

Part 2)
`y=(1)/(2)x+(9)/(2)` or
`y=0.5x+4.5`

Explanation:

we have

​(1​,5​) and ​(3​,6​)

Find the slope

The formula to calculate the slope between two points is equal to

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

substitute

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

`m=(1)/(2)`

Part 1) Find the equation in point slope form

`y-y1=m(x-x1)`

we have

`m=(1)/(2)`

`point\ (1,5)`

substitute

`y-5=(1)/(2)(x-1)`

Part 2) Find the equation in slope-intercept form

`y=mx+b`

we have

`y-5=(1)/(2)(x-1)`

isolate the variable y

`y-5=(1)/(2)x-(1)/(2)\\\\y=(1)/(2)x-(1)/(2)+5\\\\y=(1)/(2)x+(9)/(2)`