Question

. Write an equation of the line that passes through the given points use point

slope formula. (2, 1), (5,2)

Answer 1

`y = (1)/(3)x+(1)/(3)`

Explanation:

First, we need to figure out a linear equation. When given two points -
`(x_(1), y_(1))`and
`(x_(2), y_(2))` - first subtract
`y_(1)` from
`y_(2)` and and
`x_(1)` from
`x_(2)`. So in your situation, it will be
`2-1` and
`5-2`. That equals
`1` and
`3`, so your slope (how much the line moves up/down per unit) will be
`(1)/(3) x`.

Next, we need to find the y-intercept. To solve using point-slope form, we will plug our numbers in:

`y-y_(1) = m(x-x_(1))\\y-1=(1)/(3)(x-2)\\y-1=(1)/(3)x-(2)/(3)\\/+1=//+1\\y = (1)/(3)x+(1)/(3)`

So our final equation is
`y = (1)/(3)x+(1)/(3)`, which passes through both
`(2,1)` and
`(5,2)`. Hope this helps :)