Question

find the equation of the line passing through the given points. write the equation in slope-intercept form (1/5,-4) and (16/5,-9)

Answer 1

y=
`(-5)/(3)`x
`(-11)/(3)`

Explanation:

y'-y1=m(x-x1)...........(1)

given

(x1,y1)=(
`(1)/(5)`,-4)

(x2,y2)=(
`(16)/(5)`,-9)

we know that slope=m=(
`(y2-y1)/(x2-x1)`)

put values of (x1,y1) and (x2,y2)in above formula

we get

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

m=(
`(-9-(-4))/(16/5-1/5)`)

m=(
`(-9-+4))/(15/5)`)

m=(
`(-5))/(15/5)`)

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

now put slope (m) and points (x1,y1) in (1)

y-y1=m(x-x1)

y-(-4)=-5/3(x-1/5)

y+4= (-5/3)x+1/3

finally we get

y=
`('-5)/(3)`x+
`(1)/(3)`-4

y=
`(-5)/(3)`x
`(-11)/(3)`

Answer 2

`y=-(5)/(3)x-(11)/(3)`

Explanation:

We need to write the equation in slope-intercept form which passes through points (1/5,-4) and (16/5,-9)

Slope is given formula:

`m=(y_2-y_1)/(x_2-x_1)=(-9-\left(-4\right))/((16)/(5)-(1)/(5))=(-9+4)/((15)/(5))=(-5)/(3)`

Now plug the value of slope m and any one of the given point into point slope formula:

`y-y_1=m\left(x-x_1\right)`

`y-\left(-4\right)=(-5)/(3)\left(x-(1)/(5)\right)`

`y+4=-(5)/(3)x+(1)/(3)`

`y=-(5)/(3)x+(1)/(3)-4`

Now simplify this and write in slope intercept form y=mx=b

`y=-(5)/(3)x-(11)/(3)`

Hence final answer is
`y=-(5)/(3)x-(11)/(3)`