Question

find the funcation rule for thr line that passes throught thr orgin 0,0 and the poiny (-9,19) what is the function rule for the line

Answer 1

`f(x)=-(19)/(9)x`

Explanation:

Let
`(x_1,y_1)` = (0, 0)

Let
`(x_2,y_2)` = (-9, 19)

First find the slope of the function using
`\textsf{slope }m=(y_2-y_1)/(x_2-x_1)`

`\implies \textsf{slope }m=(19-0)/(-9-0)=-(19)/(9)`

Now use the point-slope form of a linear equation:
`y-y_1=m(x-x_1)`

`\implies y-19=-(19)/(9)(x+9)`

`\implies y=-(19)/(9)x`

`\implies f(x)=-(19)/(9)x`

Answer 2

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

linear function solve:

coordinates given: (0,0), (-9,19)

slope:

`\sf (y2-y1)/(x2-x1)`

`\sf (19-0)/(-9-0)`

`\sf (19)/(-9)`

equation:

`\sf y - y_2 = m(x-x_2 )`

`\sf y - 0 = (19)/(-9) (x-0 )`

`\sf y = (19)/(-9) x`

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