Question

find an equation of the line satisfying the given conditions. write the equation using function notation. Through (-20,5) and (-36, 9) And can you show me the steps?

Answer 1

The equation of the line using function notation is

`y=f(x)=-(1)/(4)x`

Explanation:

Given points are (-20,5) and (-36, 9)

Now to find the equation of the line passes through these points

Let
`(x_(1),y_(1))` and
`(x_(2),y_(2))` be the two given points (-20,5) and (-36, 9) respectively.

To find slope

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`m=(9-5)/(-36-(-20))`

`m=(4)/(-36+20)`

`m=(4)/(-16)`

`m=-(1)/(4)`

Therefore
`m=-(1)/(4)`

The equation of the line is of thr form y=mx+c

The point (-20,5) passes through the above line and
`m=-(1)/(4)`

`5=-(1)/(4)(-20)+c`

`5=5+c`

`c=0`

`y=-(1)/(4)x+0`

Therefore
`y=-(1)/(4)x`

Therefore the equation of the line using function notation is

`y=f(x)=-(1)/(4)x`